An Introduction to Proof via Inquiry-Based Learning P1C114YBXG

URI	`m2://res/P1C114YBXG`
Kind	textbook
Creators	Dana C. Ernst
Date	2026-09-17
MSC	97E50, 03-01
Scope	in

Expressions

e1: edition

Language	en
Date	2026-09-17

Contents

chapter: Acknowledgements
chapter 1: Cardinality
section 1.1: Permutations and Combinations
section 1.2: The Pigeonhole Principle
chapter 2: Definitions in Mathematics
appendix A: Elements of Style for Proofs
appendix B: Fancy Mathematical Terms
appendix C: Functions
appendix D: Induction
appendix E: Mathematics and Logic
appendix F: Introduction
appendix G: Paradoxes
chapter: Preface
appendix H: The Real Numbers
appendix I: Relations and Partitions
appendix J: Set Theory
appendix K: Three Famous Theorems

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
112V69KS33	statement	theorem, section D	ernst_ibl
1170B3GQAA	exercise	problem, section D	ernst_ibl
1368HC09M6	example	example, section 1	ernst_ibl
13G9RGHJKM	example	example, section H	ernst_ibl
Proof of $(\forall x)(A(x)\implies B(x))$	proof	skeleton, section F	ernst_ibl
15Z2VGQV23	exercise	problem, section D	ernst_ibl
16B9YC4XPY	exercise	problem, section H	ernst_ibl
18SC72KC4C	statement	theorem, section K	ernst_ibl
1B87XEXH6V	statement	theorem, section F	ernst_ibl
1D9NVSEMEE	statement	theorem, section F	ernst_ibl
1DJ1Y7TFVC	statement	theorem, section K	ernst_ibl
1EC6N3YQWQ	exercise	problem, section A	ernst_ibl
1FYD2QSVX1	exercise	problem, section H	ernst_ibl
1MQB5NB2FV	exercise	problem, section H	ernst_ibl
1SD1J14EK7	exercise	problem, section D	ernst_ibl
1WQAK85HB9	definition	definition, section J	ernst_ibl
1WVDH6QHWW	statement	theorem, section K	ernst_ibl
1XRPQYCC33	exercise	problem, section C	ernst_ibl
1ZVKVF2WP2	exercise	problem, section F	ernst_ibl
21YY1YRCWA	exercise	problem, section D	ernst_ibl
2207ZBC8PW	example	example, section A	ernst_ibl
23W4SH2GTF	exercise	question, section 1	ernst_ibl
24J9MYK8A0	exercise	problem, section D	ernst_ibl
272ZGP2AAS	exercise	problem, section D	ernst_ibl
27ZK4TM5KC	statement	theorem, section J	ernst_ibl
2MBGDYDGSD	definition	definition, section u1	ernst_ibl
2P48ERZET0	exercise	problem, section 1	ernst_ibl
2PJDTQP586	exercise	exercise, section 1.1	ernst_ibl
2QFVNE60G6	exercise	problem, section 1	ernst_ibl
Generalized Archimedean Property	statement	theorem, section u1	ernst_ibl
328H394S8Q	exercise	problem, section C	ernst_ibl
Well-Ordering Principle	statement	theorem, section K	ernst_ibl
33KXMBRJGV	statement	theorem, section 1	ernst_ibl
34R4HNJN2B	exercise	exercise, section 1.1	ernst_ibl
379BZP57K9	statement	theorem, section u1	ernst_ibl
3GZASBNESQ	exercise	problem, section G	ernst_ibl
3JJSNSAJC8	statement	theorem, section K	ernst_ibl
3KBEDCXCDW	definition	definition, section G	ernst_ibl
3SVTYNRF5M	example	example, section D	ernst_ibl
3VA5QQZ38E	exercise	question, section 1	ernst_ibl
3VC5YRZTZN	definition	definition, section C	ernst_ibl
3WDHRR53FZ	statement	theorem, section D	ernst_ibl
Proof of $A\implies B$ by contraposition	proof	skeleton, section F	ernst_ibl
Triangle Inequality	statement	theorem, section u1	ernst_ibl
3YE7MG5KH0	statement	theorem, section 1	ernst_ibl
40VCE1RV28	statement	theorem, section G	ernst_ibl
Proof of $(\forall n\in\mathbb{N})P(n)$ by Induction	proof	skeleton, section D	ernst_ibl
44Z6J42ZZ4	statement	theorem, section 1	ernst_ibl
45HZEJRMJS	statement	theorem, section 1	ernst_ibl
48QP2KKWKA	exercise	problem, section D	ernst_ibl
49CQ7BD0P0	exercise	problem, section J	ernst_ibl
4ADC9BEKPF	statement	theorem, section D	ernst_ibl
4BX45W85XR	exercise	exercise, section 1	ernst_ibl
4C03Q3GERQ	example	example, section A	ernst_ibl
4C3V5717R0	exercise	problem, section C	ernst_ibl
4CD45WX3QV	exercise	exercise, section 1.2	ernst_ibl
4CGKR5532H	statement	theorem, section K	ernst_ibl
4E1R7MVZDY	exercise	problem, section C	ernst_ibl
4E3WM66M5F	statement	theorem, section F	ernst_ibl
4FTFPXTSVP	statement	corollary, section 1	ernst_ibl
4G8HDNKB5W	definition	definition, section D	ernst_ibl
4GY3CS4YN6	exercise	problem, section K	ernst_ibl
4MWZK02TPT	proof	proof, section F	ernst_ibl
4NX8BQ5HGQ	exercise	problem, section A	ernst_ibl
4P31YQ4CGJ	exercise	problem, section 1	ernst_ibl
4P70WXTVJ9	exercise	problem, section K	ernst_ibl
4PT1Z7XX70	exercise	problem, section J	ernst_ibl
4QJK5Z3JPV	statement	theorem, section u1	ernst_ibl
Cantor's Theorem	statement	theorem, section K	ernst_ibl
4R08C64Q4K	statement	theorem, section 1	ernst_ibl
4W28VZS8NM	exercise	problem, section 1	ernst_ibl
4XMFF2Y3JY	exercise	exercise, section 1.1	ernst_ibl
4YZV6J6D41	definition	definition, section F	ernst_ibl
501BS5G9G6	exercise	problem, section 1	ernst_ibl
5234EJ350H	exercise	problem, section F	ernst_ibl
53EEKXX8MS	definition	definition, section K	ernst_ibl
54MQVGEYP4	statement	theorem, section D	ernst_ibl
56JZFMDV7Q	statement	theorem, section F	ernst_ibl
576TRF2N48	exercise	problem, section 1	ernst_ibl
587ZDXCSR8	exercise	problem, section C	ernst_ibl
5978C4RK2K	exercise	problem, section D	ernst_ibl
5B5FK4XGFY	exercise	exercise, section 1	ernst_ibl
5CCZK4EAHZ	exercise	problem, section H	ernst_ibl
5D1XH7CQ0H	statement	theorem, section K	ernst_ibl
5DN67TQ3KQ	exercise	problem, section J	ernst_ibl
5E2KSCHDF4	exercise	problem, section 1.2	ernst_ibl
5E2WGFAYTH	example	example, section D	ernst_ibl
5J7H1MBF8T	statement	theorem, section 1	ernst_ibl
5NS267HE6W	statement	theorem, section D	ernst_ibl
5R50RB9NFK	definition	definition, section H	ernst_ibl
5S1AKCQKX1	exercise	problem, section K	ernst_ibl
5T0A8APXEJ	exercise	problem, section C	ernst_ibl
5WQM9GKCRH	exercise	problem, section J	ernst_ibl
5WQN1KMDVM	definition	definition, section J	ernst_ibl
5WR1W9NG27	statement	theorem, section D	ernst_ibl
5XEZYVZC8B	example	example, section D	ernst_ibl
600N44JS4D	exercise	problem, section K	ernst_ibl
62YMD6WBSA	exercise	problem, section C	ernst_ibl
Completeness Axiom	statement	axiom, section u1	ernst_ibl
652VY0B2C3	exercise	problem, section D	ernst_ibl
Transitivity of Subsets	statement	theorem, section J	ernst_ibl
66FE9FQ7J6	exercise	problem, section K	ernst_ibl
66MS5GMWQY	exercise	problem, section D	ernst_ibl
67T0AMYKX5	statement	theorem, section J	ernst_ibl
6D2M8RMQJ2	exercise	exercise, section 1.1	ernst_ibl
6D4PHKX6ZK	statement	theorem, section J	ernst_ibl
6FS96B4AKS	statement	theorem, section K	ernst_ibl
6GJ2A3HWH4	exercise	problem, section D	ernst_ibl
6GQM3G5QTN	exercise	problem, section 1	ernst_ibl
6K9JCNSPK0	definition	definition, section u1	ernst_ibl
6KH2EKB2P8	exercise	problem, section F	ernst_ibl
Proof that a relation is transitive	proof	skeleton, section H	ernst_ibl
6NXZ060PFB	statement	corollary, section D	ernst_ibl
6PYAKSYCFG	example	example, section G	ernst_ibl
6RVGBE7V08	exercise	problem, section K	ernst_ibl
6S0VJ5NA01	exercise	problem, section F	ernst_ibl
6SDMH1KQ27	statement	theorem, section u1	ernst_ibl
6TX79WE84Y	exercise	problem, section 1	ernst_ibl
6WK5PG73GX	statement	theorem, section K	ernst_ibl
6WKJKG0CJQ	exercise	problem, section D	ernst_ibl
6WQB1X22T4	exercise	problem, section J	ernst_ibl
6XR21BXSG2	exercise	question, section 1	ernst_ibl
6YN0555N0X	proof	proof, section F	ernst_ibl
6YVKKGRNRY	statement	theorem, section F	ernst_ibl
6Z7ZPQ1C78	exercise	problem, section C	ernst_ibl
72MXJ4B4QR	exercise	problem, section K	ernst_ibl
Pigeonhole Principle	statement	theorem, section B	ernst_ibl
74WF4RYEW2	exercise	problem, section C	ernst_ibl
75XTE4GQAC	exercise	problem, section u1	ernst_ibl
De Morgan's Law	statement	theorem, section D	ernst_ibl
Proof of $(\exists x)P(x)$ by Contradiction	proof	skeleton, section F	ernst_ibl
7F5JHAFDZG	exercise	problem, section F	ernst_ibl
7F6NN1RAGT	exercise	problem, section 1	ernst_ibl
7FAAN66DV4	exercise	exercise, section 1.1	ernst_ibl
7JX67FDRDP	exercise	problem, section D	ernst_ibl
7KTVQBH6DJ	exercise	problem, section I	ernst_ibl
7N6SRR28NR	exercise	problem, section C	ernst_ibl
7RP5XY7VQQ	statement	theorem, section u1	ernst_ibl
7VNV5AY9JJ	definition	definition, section F	ernst_ibl
7Z19MD2FB9	definition	definition, section 1	ernst_ibl
7ZPM823J8R	exercise	problem, section C	ernst_ibl
814809T2GY	exercise	problem, section H	ernst_ibl
83ZC966YD6	example	example, section F	ernst_ibl
8582MAZFKH	definition	definition, section D	ernst_ibl
868R00CX37	exercise	problem, section H	ernst_ibl
87JF3SEEZD	statement	theorem, section K	ernst_ibl
88KPKF89B6	statement	theorem, section C	ernst_ibl
8DWFMFCZRV	statement	corollary, section D	ernst_ibl
8FS1953Q0S	exercise	problem, section F	ernst_ibl
8K2KY6XM4C	exercise	problem, section F	ernst_ibl
8K6NGQ7BVM	statement	theorem, section u1	ernst_ibl
8MY3DG0272	statement	theorem, section F	ernst_ibl
8Q3R790XTJ	exercise	exercise, section 1	ernst_ibl
8QM9PBX2P5	statement	theorem, section 1	ernst_ibl
8RNVYC24Z2	proof	proof, section F	ernst_ibl
8SBWXK76TE	statement	theorem, section G	ernst_ibl
Direct Proof of $(\exists x)P(x)$	proof	skeleton, section F	ernst_ibl
8T7D6FJ73E	statement	theorem, section u1	ernst_ibl
8VWQFRYT4G	exercise	problem, section D	ernst_ibl
8X9ZC0B927	statement	corollary, section F	ernst_ibl
92PC2BKSBE	exercise	problem, section 1	ernst_ibl
92V0M8XP91	example	example, section H	ernst_ibl
Principle of Mathematical Induction	statement	theorem, section F	ernst_ibl
Proof of $A\implies B$ by direct proof	proof	skeleton, section F	ernst_ibl
96K9KAQGAM	proof	proof, section C	ernst_ibl
9731VX742P	exercise	problem, section 1	ernst_ibl
98ZEZ101V1	statement	theorem, section D	ernst_ibl
9BMAP6G9S0	definition	definition, section 1	ernst_ibl
9BZRJM2RDX	statement	theorem, section 1	ernst_ibl
Proof of $A\implies B$ by contradiction	proof	skeleton, section F	ernst_ibl
9KGMTN6WYQ	statement	theorem, section 1	ernst_ibl
9KS531EGCR	exercise	problem, section 1	ernst_ibl
9QC313EMXC	exercise	problem, section H	ernst_ibl
9RM5Y8NXS8	statement	theorem, section K	ernst_ibl
9ZHGF99GZM	example	example, section 1	ernst_ibl
Principle of Mathematical Induction	statement	theorem, section D	ernst_ibl
A1985EZDP0	statement	theorem, section u1	ernst_ibl
A1VXXDN3Z2	exercise	problem, section H	ernst_ibl
A3N33G0AHR	exercise	problem, section I	ernst_ibl
A4AJMJRWZV	statement	theorem, section C	ernst_ibl
A5J1K040BW	exercise	problem, section 1	ernst_ibl
Axiom of Induction	statement	axiom, section D	ernst_ibl
AB4BJD51N6	statement	corollary, section F	ernst_ibl
AE2K6SKG8V	definition	definition, section J	ernst_ibl
AEHBXCB2WR	example	example, section H	ernst_ibl
AM6A3P3FFK	definition	definition, section G	ernst_ibl
AN9XKJ3RDQ	exercise	problem, section G	ernst_ibl
AQDK4Z949S	definition	definition, section 1	ernst_ibl
Distribution of Union and Intersection	statement	theorem, section J	ernst_ibl
ARXZGC505S	statement	theorem, section u1	ernst_ibl
ASF26GQTVQ	exercise	problem, section 1	ernst_ibl
Proof of $(\forall x)P(x)$ by Contradiction	proof	skeleton, section F	ernst_ibl
ASNV82EAQ6	exercise	problem, section D	ernst_ibl
ATY0AJBSMQ	exercise	problem, section 1	ernst_ibl
Proof that a relation is symmetric	proof	skeleton, section H	ernst_ibl
AXTP62EKBH	statement	theorem, section u1	ernst_ibl
B0JB7WS7T1	exercise	problem, section D	ernst_ibl
B0PFFNY8YS	proof	proof, section F	ernst_ibl
B26XRWYT7D	exercise	problem, section D	ernst_ibl
B2X3VK0XD9	statement	theorem, section u1	ernst_ibl
B3S3M4KMM0	statement	theorem, section F	ernst_ibl
BD3SFXGAR7	proof	proof, section F	ernst_ibl
BEF3109MJE	exercise	problem, section 1	ernst_ibl
BESP04P47G	exercise	problem, section 1	ernst_ibl
BGPYYQ12ZR	statement	theorem, section 1	ernst_ibl
BJ5XC4J0WQ	exercise	problem, section G	ernst_ibl
BJ96ESMFJE	statement	theorem, section F	ernst_ibl
BQC2F1P6VG	proof	proof, section H	ernst_ibl
BQCNP67QFG	definition	definition, section H	ernst_ibl
BRCZBVZM79	statement	theorem, section D	ernst_ibl
BRMCX3PQ1S	exercise	problem, section J	ernst_ibl
BV65K7GY57	exercise	problem, section 1	ernst_ibl
BWNG44BGAD	exercise	problem, section F	ernst_ibl
BXRV099JER	statement	theorem, section u1	ernst_ibl
BY5X70E2JM	proof	proof, section 1	ernst_ibl
BZJKJ4T13E	exercise	exercise, section 1.1	ernst_ibl
C0ZFZ11AYH	definition	definition, section D	ernst_ibl
C2RQND0Y8R	exercise	problem, section J	ernst_ibl
C347XCHEQF	exercise	problem, section D	ernst_ibl
C45RM4YC8W	statement	theorem, section 1	ernst_ibl
C55QECBFQ6	statement	theorem, section F	ernst_ibl
C8MCGQ74NP	example	example, section 1	ernst_ibl
C9THB9NRKG	exercise	problem, section G	ernst_ibl
CA73AP2R7S	exercise	problem, section D	ernst_ibl
CAE3CJZKH0	statement	theorem, section u1	ernst_ibl
CAPZN7H2S8	exercise	exercise, section 1.1	ernst_ibl
CB1BKJS0Z5	statement	theorem, section D	ernst_ibl
CDG7BJD3WN	statement	theorem, section 1	ernst_ibl
CETSMP9TE5	exercise	problem, section C	ernst_ibl
CHG6HC0VNV	exercise	problem, section u1	ernst_ibl
CHMW16K0CB	exercise	problem, section D	ernst_ibl
CHSVBSMNC4	statement	theorem, section D	ernst_ibl
CK9NST4M8N	exercise	problem, section D	ernst_ibl
CSDR0JZ2TN	definition	definition, section D	ernst_ibl
CSFH55C6FN	exercise	problem, section 1	ernst_ibl
CTDG9BJB1N	exercise	problem, section D	ernst_ibl
CY2DMJA06Y	statement	theorem, section D	ernst_ibl
CYNK1225MP	statement	theorem, section D	ernst_ibl
CZQHC3E6RV	exercise	problem, section K	ernst_ibl
D0A7RAWYYW	statement	theorem, section K	ernst_ibl
D3J7EYRGX1	statement	theorem, section A	ernst_ibl
D6BC6EKGP0	definition	definition, section A	ernst_ibl
Proof that a relation is reflexive	proof	skeleton, section H	ernst_ibl
D94C10004Z	example	example, section D	ernst_ibl
DCB1HE11SW	example	example, section H	ernst_ibl
DESB92SP3Q	definition	definition, section J	ernst_ibl
DFA0JRDV81	exercise	problem, section D	ernst_ibl
DFGVM1HF7H	statement	theorem, section A	ernst_ibl
DJAKJ9KGVH	statement	theorem, section G	ernst_ibl
DMGYQ2S9NV	statement	theorem, section K	ernst_ibl
Proof of $(\forall n\in\mathbb{N})P(n)$ by Complete Induction	proof	skeleton, section 1	ernst_ibl
DQR28HRFT6	definition	definition, section J	ernst_ibl
DSVPY9630B	statement	theorem, section F	ernst_ibl
DTSSFZKE70	exercise	problem, section K	ernst_ibl
DV5T0RZM4M	statement	theorem, section u1	ernst_ibl
DV7SXH94X7	statement	theorem, section D	ernst_ibl
DW6WVAH7Q8	exercise	problem, section D	ernst_ibl
DWM5WCBQXF	statement	theorem, section B	ernst_ibl
DX16CS4DGT	statement	theorem, section D	ernst_ibl
DYVRBAFCSW	exercise	problem, section D	ernst_ibl
DZ31Q52TK7	statement	theorem, section F	ernst_ibl
DZ88KKT8WZ	statement	theorem, section F	ernst_ibl
DZNFDTTNQ0	exercise	problem, section D	ernst_ibl
E0TDM8SWTD	exercise	problem, section J	ernst_ibl
E3CHJZ1YMB	proof	proof, section H	ernst_ibl
E3K3GY5Q3H	exercise	problem, section 1	ernst_ibl
E70K0FEP6X	statement	theorem, section K	ernst_ibl
E87ZGYXWFV	statement	theorem, section 1	ernst_ibl
E98FGS41PC	exercise	problem, section 1	ernst_ibl
EAQ1SK92WQ	statement	theorem, section J	ernst_ibl
EBQW361WG3	exercise	problem, section D	ernst_ibl
EC8XK0SQ6E	exercise	problem, section 1	ernst_ibl
Proof of $(\forall n \in \mathbb{Z})(n \geq a \implies P(n))$ by Induction	proof	skeleton, section F	ernst_ibl
EDZ3DX8AWB	exercise	problem, section 1	ernst_ibl
EEWTZR50RH	exercise	problem, section 1	ernst_ibl
EGFJZ2KWJV	example	example, section D	ernst_ibl
EKX2CM07KT	definition	definition, section u1	ernst_ibl
EMNNDTG93C	statement	theorem, section u1	ernst_ibl
ENN7P064NN	exercise	exercise, section 1	ernst_ibl
EQTYNXPV7W	exercise	problem, section A	ernst_ibl
ERV36BAQEM	definition	definition, section 1	ernst_ibl
ES1FFVEQHB	exercise	problem, section K	ernst_ibl
ESPJECKB3C	exercise	problem, section 1	ernst_ibl
EV5800ESE6	example	example, section H	ernst_ibl
EV7R85V855	exercise	problem, section D	ernst_ibl
EZMB5AS4SK	exercise	exercise, section 1.2	ernst_ibl
F1QGC23K2B	statement	theorem, section D	ernst_ibl
F4QQRTNY04	definition	definition, section J	ernst_ibl
F4XSC8AYFT	exercise	problem, section D	ernst_ibl
F4Y80HCP6E	statement	theorem, section J	ernst_ibl
Archimedean Property	statement	theorem, section u1	ernst_ibl
F8RASP53WG	exercise	problem, section 1	ernst_ibl
FAGFEMF3S4	statement	theorem, section J	ernst_ibl
FBG4FS5XZN	statement	theorem, section D	ernst_ibl
FCFJEHTHFN	definition	definition, section D	ernst_ibl
FFKAD40G68	statement	theorem, section F	ernst_ibl
FGYG1E50WJ	statement	theorem, section 1	ernst_ibl
FJGC330ZQC	statement	theorem, section K	ernst_ibl
FK10EZMQP5	exercise	problem, section D	ernst_ibl
FNTSG0BNMA	definition	definition, section K	ernst_ibl
FPB1YN1DP7	definition	definition, section 1.1	ernst_ibl
FQ13G1XT1D	exercise	problem, section G	ernst_ibl
FQ3HBW38XS	exercise	problem, section F	ernst_ibl
FR0XWA7KPW	statement	theorem, section 1	ernst_ibl
FT7KGSR8GK	exercise	problem, section u1	ernst_ibl
FWS7J1JDWV	statement	theorem, section 1	ernst_ibl
FX35ZBKT55	statement	theorem, section 1	ernst_ibl
FXXDC2MYE0	definition	definition, section K	ernst_ibl
G0F35TR76P	exercise	problem, section C	ernst_ibl
G0NE8Q4G5X	statement	theorem, section B	ernst_ibl
G2MTQCERAQ	statement	theorem, section u1	ernst_ibl
G5T3YA272C	exercise	problem, section 1	ernst_ibl
G6RMBN1PGG	exercise	problem, section H	ernst_ibl
G9QW4Q68T3	exercise	problem, section D	ernst_ibl
GAFE212X5S	exercise	problem, section 1	ernst_ibl
GCA7ZAF0R0	definition	definition, section J	ernst_ibl
GCBJ5ZRA5X	exercise	problem, section 1	ernst_ibl
Fundamental Theorem of Arithmetic	statement	theorem, section C	ernst_ibl
GN0VS8MW8Z	definition	definition, section H	ernst_ibl
GP1T3PEDAM	exercise	problem, section 1	ernst_ibl
GRWFE4D9RB	statement	theorem, section J	ernst_ibl
GSWNSSH2WE	exercise	exercise, section 1.1	ernst_ibl
Direct Proof of $(\exists! x)P(x)$	proof	skeleton, section F	ernst_ibl
GYV9G050WX	statement	theorem, section 1	ernst_ibl
H2PW5ZQ6GK	exercise	exercise, section 1.1	ernst_ibl
Intermediate Value Theorem	statement	theorem, section 1	ernst_ibl
H394VBQX94	exercise	problem, section D	ernst_ibl
H4XPRSQ2HA	exercise	problem, section C	ernst_ibl
H56QH5KQ55	exercise	problem, section C	ernst_ibl
Order Axioms	statement	axioms, section u1	ernst_ibl
HA16C39M8T	exercise	problem, section u1	ernst_ibl
HBCFD52B9B	definition	definition, section C	ernst_ibl
HBHZMV0SCV	statement	theorem, section u1	ernst_ibl
HCH0GP9PWP	definition	definition, section A	ernst_ibl
HEAR9SQ3XB	definition	definition, section u1	ernst_ibl
HEFVG3JA9H	exercise	problem, section 1	ernst_ibl
HF8QYGQA3V	definition	definition, section C	ernst_ibl
HHP5S6JT6P	statement	theorem, section K	ernst_ibl
HNH71X6WB1	exercise	problem, section D	ernst_ibl
HNJHSBEQZ2	exercise	problem, section D	ernst_ibl
HTRCCNXY00	exercise	problem, section G	ernst_ibl
HW0FQ2F7V5	exercise	problem, section H	ernst_ibl
HX4EDE2W7M	example	example, section D	ernst_ibl
HYK0F07WDP	statement	theorem, section F	ernst_ibl
HZZ0XJ7EKF	statement	theorem, section D	ernst_ibl
J03JW3Q51H	exercise	problem, section D	ernst_ibl
J0R940MTJH	statement	theorem, section 1	ernst_ibl
Axiom of Choice	statement	axiom, section C	ernst_ibl
J2SETYW98K	statement	theorem, section u1	ernst_ibl
J3ACSF5HHR	statement	theorem, section 1	ernst_ibl
J6JTNA5X8A	exercise	problem, section D	ernst_ibl
J7TA9ZFK59	statement	theorem, section B	ernst_ibl
J983J1MFC9	definition	definition, section K	ernst_ibl
J9K4MARSVK	exercise	problem, section 1	ernst_ibl
JAZHKXQ4CJ	definition	definition, section K	ernst_ibl
JCW5PC1PQH	exercise	problem, section D	ernst_ibl
JMT147VHD0	statement	theorem, section K	ernst_ibl
JRKMKT2XH3	statement	theorem, section K	ernst_ibl
JV6BXWHBRK	exercise	problem, section G	ernst_ibl
JXYE0SR2XC	definition	definition, section D	ernst_ibl
JY6B60EBMA	example	example, section H	ernst_ibl
K0Z62VFZ7A	statement	corollary, section J	ernst_ibl
K3N8E7WSDM	statement	theorem, section u1	ernst_ibl
KBG7SB930K	exercise	problem, section C	ernst_ibl
KC2037JQ7J	definition	definition, section C	ernst_ibl
KHR4YE4DXR	exercise	problem, section 1	ernst_ibl
KK2WE47H9N	exercise	exercise, section 1.1	ernst_ibl
KKK4DW7TPG	statement	corollary, section D	ernst_ibl
KN2TXD9TYN	exercise	problem, section 1	ernst_ibl
KNQSDJ6QAS	statement	theorem, section D	ernst_ibl
KNVTCT57TV	exercise	problem, section D	ernst_ibl
KQ1279P3CZ	proof	proof, section F	ernst_ibl
KQGZGJZY4A	exercise	problem, section 1	ernst_ibl
KTCW02GBZY	statement	theorem, section K	ernst_ibl
KV1PF7QV0Q	example	example, section H	ernst_ibl
KWW5KH07V9	exercise	problem, section K	ernst_ibl
KZ2S03FS4V	exercise	problem, section 1	ernst_ibl
KZNX7HC8AZ	exercise	problem, section K	ernst_ibl
KZTE0VGB64	proof	proof, section F	ernst_ibl
M061HJN2DE	statement	theorem, section J	ernst_ibl
M1FJZKC8HH	statement	theorem, section F	ernst_ibl
M290H4Y4RA	exercise	problem, section G	ernst_ibl
M296KWQYN2	exercise	problem, section C	ernst_ibl
M2A50X4D6Y	exercise	problem, section C	ernst_ibl
M3T5MQ7NWY	statement	theorem, section F	ernst_ibl
M4551RQ2C1	exercise	problem, section A	ernst_ibl
M4HBXQ83RF	exercise	problem, section 1	ernst_ibl
M4HK7PS7B9	statement	theorem, section u1	ernst_ibl
M4STBZ4TBS	exercise	exercise, section 1.1	ernst_ibl
M9QAS7HB53	example	example, section G	ernst_ibl
MACVC5M8QX	exercise	problem, section H	ernst_ibl
MBZRT0ZCJG	proof	proof, section F	ernst_ibl
MD0JHR9Z7Y	exercise	problem, section F	ernst_ibl
MD4KV4H263	statement	theorem, section 1	ernst_ibl
De Morgan's Law	statement	theorem, section J	ernst_ibl
MDCNGZ739T	exercise	problem, section F	ernst_ibl
MEG45GCXGM	statement	theorem, section K	ernst_ibl
MGYMK6JVSP	example	example, section D	ernst_ibl
MHZ1KFTMZ8	statement	theorem, section u1	ernst_ibl
MKABZJFMVB	statement	theorem, section B	ernst_ibl
MN7P450WGM	exercise	problem, section F	ernst_ibl
MNKHCSHHG4	statement	theorem, section F	ernst_ibl
MWXZ1Z9FTA	example	example, section D	ernst_ibl
N0A7ED28VE	exercise	problem, section H	ernst_ibl
N0GGQAHAY1	definition	definition, section 1.1	ernst_ibl
N0PAMBVYS2	exercise	problem, section K	ernst_ibl
N2EEN6N061	exercise	problem, section A	ernst_ibl
N43NMM0DN1	statement	theorem, section J	ernst_ibl
N6YZCXKKRK	exercise	problem, section G	ernst_ibl
Field Axioms	statement	axioms, section u1	ernst_ibl
N8WRQ5JM1D	statement	theorem, section 1	ernst_ibl
NC12SNJB0D	example	example, section F	ernst_ibl
ND264JEVWM	statement	theorem, section G	ernst_ibl
ND85EE0PDS	exercise	problem, section 1	ernst_ibl
NDCMEZY0Y7	exercise	problem, section D	ernst_ibl
NEBYJ9K0W5	statement	theorem, section u1	ernst_ibl
NF89FK30KF	exercise	problem, section D	ernst_ibl
NHFWF057V4	statement	theorem, section J	ernst_ibl
NHT6R3J155	example	example, section D	ernst_ibl
NKPD82857K	exercise	problem, section J	ernst_ibl
NQKV7DFC87	exercise	problem, section A	ernst_ibl
NSP6J31V8M	exercise	problem, section D	ernst_ibl
NTZXBK3GHX	statement	theorem, section u1	ernst_ibl
NVH7R4BXH5	proof	proof, section F	ernst_ibl
NW1Y0VY73M	statement	theorem, section F	ernst_ibl
NYN9RMKHZ7	exercise	problem, section F	ernst_ibl
NYY6C7Z3VW	definition	definition, section D	ernst_ibl
Principle of Complete Mathematical Induction	statement	theorem, section 1	ernst_ibl
P01SVMTQY4	exercise	problem, section A	ernst_ibl
Generalized Distribution of Union and Intersection	statement	theorem, section C	ernst_ibl
P0BCQCS7YZ	statement	theorem, section u1	ernst_ibl
P0HXJPET6P	exercise	problem, section K	ernst_ibl
P0Y6C08TM5	statement	theorem, section F	ernst_ibl
P17XV9ZWXH	exercise	problem, section D	ernst_ibl
P2205YN1C1	example	example, section H	ernst_ibl
P289VF1XHG	exercise	problem, section 1	ernst_ibl
P2QV31Z4Y0	exercise	problem, section F	ernst_ibl
P3E245P1Q8	exercise	problem, section 1	ernst_ibl
P4HA9YJ96R	exercise	problem, section D	ernst_ibl
P5YQ6MNTVY	statement	theorem, section F	ernst_ibl
P6X7AY2TA7	statement	theorem, section K	ernst_ibl
P8SYYG8M6X	example	example, section D	ernst_ibl
PAF9YTJPQ1	exercise	problem, section J	ernst_ibl
PC22603S5C	example	example, section 1	ernst_ibl
PC9VEE686G	exercise	problem, section D	ernst_ibl
PCJSMNX2VQ	exercise	problem, section 1	ernst_ibl
PCSACCGAYY	proof	proof, section D	ernst_ibl
PDF9GRHYAH	exercise	problem, section G	ernst_ibl
PEHM6VNQPR	exercise	problem, section D	ernst_ibl
PESYKFP3N3	statement	theorem, section 1	ernst_ibl
PEVJFE0T78	proof	proof, section D	ernst_ibl
PMK1C0YKYJ	definition	definition, section D	ernst_ibl
PMR2GMQ99D	exercise	problem, section 1	ernst_ibl
PNSN83G7T6	exercise	problem, section F	ernst_ibl
PS3YAPTC35	exercise	problem, section D	ernst_ibl
PSJH1M4JYQ	statement	theorem, section F	ernst_ibl
PTD0EAW55H	statement	corollary, section 1	ernst_ibl
PXK660AQBW	statement	theorem, section u1	ernst_ibl
PZRAW8H4M8	statement	theorem, section D	ernst_ibl
Q0W15Y62RG	exercise	problem, section 1	ernst_ibl
Q1EAGXMTDF	statement	theorem, section F	ernst_ibl
Q2374R2V3X	statement	corollary, section K	ernst_ibl
Q7EB8KXBEY	definition	definition, section 1	ernst_ibl
Q9Z8T0FA8M	exercise	problem, section D	ernst_ibl
QCX2MHS6WW	example	example, section D	ernst_ibl
Generalized De Morgan's Law	statement	theorem, section C	ernst_ibl
QET6S1633Z	definition	definition, section J	ernst_ibl
QFA50JPG6E	definition	definition, section D	ernst_ibl
Reverse Triangle Inequality	statement	theorem, section u1	ernst_ibl
Euclid's Lemma	statement	theorem, section C	ernst_ibl
QGGPPYFQAP	exercise	problem, section D	ernst_ibl
QGNQ7HNQB8	statement	theorem, section F	ernst_ibl
QHD98T81QK	exercise	problem, section K	ernst_ibl
QJCF4891KE	statement	theorem, section 1	ernst_ibl
QJG3BR06MY	statement	theorem, section 1	ernst_ibl
QR7JQGB3C9	exercise	problem, section D	ernst_ibl
QSJJE9QPDX	definition	definition, section D	ernst_ibl
Direct Proof of $(\forall x)P(x)$	proof	skeleton, section F	ernst_ibl
QTD7DVMYV3	definition	definition, section F	ernst_ibl
QVAG7W0E3M	definition	definition, section u1	ernst_ibl
QWVC6NKRHF	exercise	problem, section D	ernst_ibl
QWX6EK3GSW	statement	theorem, section F	ernst_ibl
R1WNY2YYCE	exercise	problem, section D	ernst_ibl
R2J1EJK834	exercise	problem, section J	ernst_ibl
R3PF7K8C2F	exercise	problem, section F	ernst_ibl
R4N6FRN9FJ	exercise	problem, section D	ernst_ibl
R786VPMV1Z	definition	definition, section F	ernst_ibl
R7DTZ9AGQS	definition	definition, section K	ernst_ibl
R7KK0PAW7T	exercise	problem, section C	ernst_ibl
RB4BAN1XAN	exercise	problem, section G	ernst_ibl
RC0XEKB3HV	definition	definition, section 1	ernst_ibl
RDNMENQ3Z1	exercise	problem, section 1	ernst_ibl
REJRWAXX25	definition	definition, section D	ernst_ibl
RFZM84689K	exercise	question, section 1	ernst_ibl
RGEQ113QRV	definition	definition, section F	ernst_ibl
RJNKHQG6X3	exercise	problem, section G	ernst_ibl
RKANDFFHJP	statement	theorem, section u1	ernst_ibl
RQ9THSRDVV	exercise	problem, section 1	ernst_ibl
RR1Q0Y121T	exercise	problem, section u1	ernst_ibl
RTA1YVDXM8	exercise	problem, section D	ernst_ibl
RWWT9YXZJH	definition	definition, section F	ernst_ibl
RX8FA85EJT	exercise	problem, section K	ernst_ibl
RZG6EP4WGJ	exercise	problem, section D	ernst_ibl
S0PZK22S2Q	exercise	problem, section G	ernst_ibl
S2N5PQM062	example	example, section H	ernst_ibl
S2QCYTV997	definition	definition, section 1	ernst_ibl
S3Q163VWKH	statement	theorem, section K	ernst_ibl
S48HF3H5JT	statement	theorem, section u1	ernst_ibl
S4E8K6DFK8	exercise	problem, section C	ernst_ibl
S5T7CE4AQ5	statement	theorem, section u1	ernst_ibl
S7NX2TNR5K	proof	proof, section F	ernst_ibl
S7Y9YWR20M	definition	definition, section B	ernst_ibl
S90X2NVD42	statement	theorem, section F	ernst_ibl
S9C1F5N679	example	example, section D	ernst_ibl
S9VSWR8TMG	example	example, section D	ernst_ibl
SC3178JTG4	exercise	problem, section 1	ernst_ibl
SDNWSQRBR2	exercise	problem, section J	ernst_ibl
SE7FHF5CZV	exercise	problem, section F	ernst_ibl
SE7SD2944Y	exercise	problem, section D	ernst_ibl
SEYNDTSSP0	statement	theorem, section D	ernst_ibl
SGD1YKMJYT	exercise	problem, section G	ernst_ibl
SH3KN4X9RZ	definition	definition, section u1	ernst_ibl
SH5P0S0W15	exercise	problem, section K	ernst_ibl
SH89TXMNTY	exercise	exercise, section 1.1	ernst_ibl
SHQFG0ZWBC	proof	proof, section F	ernst_ibl
SN9T71XQBN	exercise	problem, section 1	ernst_ibl
SSD8S52GVF	exercise	problem, section D	ernst_ibl
SSDDG1W0YN	exercise	problem, section D	ernst_ibl
SXARNM6CQY	statement	theorem, section D	ernst_ibl
T005PQG23S	exercise	problem, section D	ernst_ibl
T0XH8E8A7S	exercise	problem, section H	ernst_ibl
T2GM2R0H4Z	statement	theorem, section G	ernst_ibl
T3V2CD7GAR	definition	definition, section D	ernst_ibl
T4PPX21QXK	exercise	question, section 1	ernst_ibl
T541RYYQ1R	definition	definition, section J	ernst_ibl
T6423MYVWG	exercise	problem, section D	ernst_ibl
T6FDWEB5ZS	exercise	problem, section 1	ernst_ibl
TFB4VMJ074	exercise	problem, section D	ernst_ibl
TK8EDN5D84	exercise	problem, section C	ernst_ibl
TMACC8NZRW	exercise	problem, section I	ernst_ibl
TPHDPACW0T	exercise	problem, section K	ernst_ibl
TPJ3K6S96R	exercise	problem, section H	ernst_ibl
TQ5VT73WKA	exercise	problem, section H	ernst_ibl
TSPRWBNBKC	statement	theorem, section u1	ernst_ibl
TWPWPVQNXZ	statement	theorem, section 1	ernst_ibl
V1HW648NZN	example	example, section F	ernst_ibl
V1MXB0FJ9A	statement	theorem, section K	ernst_ibl
V39EW7JCA1	statement	theorem, section J	ernst_ibl
V57TP6WM5J	statement	theorem, section F	ernst_ibl
V5YW7HC1AZ	statement	theorem, section F	ernst_ibl
V7MT65KQCR	exercise	problem, section D	ernst_ibl
V877BEMV3Y	definition	definition, section u1	ernst_ibl
Proof that a function is injective	proof	skeleton, section D	ernst_ibl
VC3M40ASCP	definition	definition, section G	ernst_ibl
VC6WE6VKM0	exercise	problem, section A	ernst_ibl
VC737P346J	exercise	question, section 1	ernst_ibl
VD69BWKXP4	statement	theorem, section K	ernst_ibl
VEKXXBEC8S	exercise	problem, section 1	ernst_ibl
VEYA29N3PC	statement	theorem, section F	ernst_ibl
VFS983HTJ9	exercise	problem, section C	ernst_ibl
VJ3XVRKTWB	exercise	problem, section C	ernst_ibl
VMYMHDSXVD	statement	theorem, section K	ernst_ibl
VNB6S9F3YY	exercise	problem, section 1.1	ernst_ibl
VNEDBN0D1H	definition	definition, section D	ernst_ibl
VPTD67C85M	exercise	problem, section D	ernst_ibl
Special Case of B\'ezout's Lemma	statement	theorem, section C	ernst_ibl
VYMH8B5Q69	exercise	problem, section F	ernst_ibl
VYPT78S776	proof	proof, section H	ernst_ibl
VZ3WCBSP6G	definition	definition, section 1	ernst_ibl
Division Algorithm	statement	theorem, section C	ernst_ibl
W37ZS22C58	statement	theorem, section G	ernst_ibl
W45N213BYH	example	example, section H	ernst_ibl
W5G1PDVXYN	statement	theorem, section F	ernst_ibl
W651XZP3PZ	statement	theorem, section 1	ernst_ibl
WAJDR46SWR	proof	proof, section D	ernst_ibl
WBBN09KM1B	exercise	problem, section 1	ernst_ibl
WC4ZDVT84T	exercise	problem, section F	ernst_ibl
WDXDRXMXZZ	exercise	problem, section 1	ernst_ibl
WKSZ60AGQ3	statement	theorem, section D	ernst_ibl
WM9H7ZS4VN	example	example, section H	ernst_ibl
WP9X2ZW42Y	example	example, section H	ernst_ibl
WS1BWQBQJZ	exercise	problem, section 1	ernst_ibl
WS6XC535ZY	exercise	exercise, section 1.1	ernst_ibl
WT6KWSFATZ	exercise	problem, section C	ernst_ibl
WVTZEFZNA5	exercise	problem, section J	ernst_ibl
WWCVKXH7DG	exercise	exercise, section 1.1	ernst_ibl
X078102R0H	definition	definition, section D	ernst_ibl
X1KMKDXR6P	statement	theorem, section K	ernst_ibl
X3M6QTS4S0	proof	proof, section D	ernst_ibl
X3QFXPKQHJ	statement	corollary, section D	ernst_ibl
X75CTGV36X	statement	theorem, section F	ernst_ibl
X9HBKGRFR6	example	example, section G	ernst_ibl
XABFVZ8NMJ	statement	corollary, section K	ernst_ibl
XE30QBT02Y	exercise	problem, section A	ernst_ibl
XJYWY0VN9Z	statement	corollary, section G	ernst_ibl
XM3AWFNKV4	exercise	problem, section D	ernst_ibl
XRVT84ZJR6	exercise	problem, section H	ernst_ibl
XV1Y9G2QXJ	statement	theorem, section D	ernst_ibl
XW72Z72B5T	definition	definition, section D	ernst_ibl
XX45Z7DF7Y	statement	theorem, section u1	ernst_ibl
XXJWZ7G3D3	statement	theorem, section u1	ernst_ibl
XYM1WXKCXS	definition	definition, section D	ernst_ibl
XZCARF570K	exercise	exercise, section 1.1	ernst_ibl
XZVEQPADT6	exercise	problem, section D	ernst_ibl
Y0Y3MS2CWR	exercise	problem, section 1	ernst_ibl
Y28YN8AFX2	statement	theorem, section B	ernst_ibl
Y2F08QM0BX	exercise	problem, section K	ernst_ibl
Y3TBKGFFHS	statement	theorem, section D	ernst_ibl
Y46PV8GYNM	exercise	exercise, section 1	ernst_ibl
Y7N7ZHTK66	definition	definition, section D	ernst_ibl
Y80X74XP4K	definition	definition, section C	ernst_ibl
Y8VE4WF4DP	statement	theorem, section B	ernst_ibl
Y9QTM6M8FK	statement	theorem, section 1	ernst_ibl
YAHTNCDHC2	exercise	problem, section 1	ernst_ibl
YE3M8FFXAD	statement	theorem, section u1	ernst_ibl
YENBXPQ2JR	exercise	problem, section C	ernst_ibl
YFWX33GTB4	exercise	problem, section 1	ernst_ibl
YG90PGH23S	example	example, section F	ernst_ibl
YGWZ96N7KA	statement	theorem, section 1	ernst_ibl
YJS0VNNMMA	definition	definition, section B	ernst_ibl
YMH52F64H1	exercise	problem, section G	ernst_ibl
Proof of $P$ by contradiction	proof	skeleton, section F	ernst_ibl
YQSQ6NBFGV	statement	theorem, section F	ernst_ibl
YQX09JKPAW	exercise	problem, section G	ernst_ibl
YRT5T2JXDY	statement	theorem, section F	ernst_ibl
YS3MM4YV8V	statement	theorem, section 1	ernst_ibl
YT4M7DD71F	exercise	problem, section D	ernst_ibl
YTJXMVAKHS	statement	theorem, section u1	ernst_ibl
YZWKMMB4W8	definition	definition, section D	ernst_ibl
Proof that a function is surjective	proof	skeleton, section D	ernst_ibl
Z0R22QAP7V	statement	theorem, section K	ernst_ibl
Z10Z5HN966	exercise	problem, section D	ernst_ibl
Z1V3HNGXVS	exercise	problem, section F	ernst_ibl
Z3GERWQ1R1	definition	definition, section D	ernst_ibl
De Morgan's Law	exercise	problem, section D	ernst_ibl
Z9B4AWJPKC	statement	theorem, section F	ernst_ibl
Z9Y1H41ENR	statement	theorem, section 1	ernst_ibl
ZA6TSM6ZMP	statement	corollary, section u1	ernst_ibl
ZBC3JKS0VS	exercise	problem, section D	ernst_ibl
ZBDE8XY2SF	statement	theorem, section C	ernst_ibl
ZBRVSPWH1N	exercise	problem, section A	ernst_ibl
ZCDM4CKFSA	exercise	problem, section G	ernst_ibl
ZFB77GWGQZ	statement	theorem, section F	ernst_ibl
ZFW0T0FFGP	statement	theorem, section F	ernst_ibl
ZH4QMP7ZH2	statement	theorem, section J	ernst_ibl
ZJCTDREC11	exercise	problem, section D	ernst_ibl
ZV055G511T	exercise	problem, section C	ernst_ibl
ZZBHT7MBPY	exercise	problem, section 1	ernst_ibl

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ernst_ibl: ernst_ibl (work)