---
tag: F2C174HHSE
kind: concept
name: Semiorder
msc: [06A06, 91B08]
specializes: [VSNQV29KFJ]
sources:
  - url: https://en.wikipedia.org/wiki/Semiorder
same_as:
  wikidata: Q7449567
  wikipedia: Semiorder
---

## Summary

A semiorder is a strict partial order in which one element is below another when it is smaller by more than a fixed threshold.
Semiorders model preferences in which small differences cannot be noticed.
They are the [[interval orders|VSNQV29KFJ]] that can be represented by intervals of the same length.

## Explanations

### L1 human

A person may not taste the difference between coffee with $10$ grains of sugar and coffee with $11$ grains.
Yet the same person prefers $10$ grains to $500$ grains.
So "not noticeably different" is not transitive, while "noticeably less sweet" is still an order.
On the real numbers, the relation $x \prec y$ when $x + 1 < y$ is a semiorder of this kind.