Definition

A principle in mathematics and logic stating that two functions or sets are considered equal if they have the same elements or produce the same results for the same inputs.

Example

According to the axiom of extensionality, two sets are equal if they contain exactly the same elements.

Conversation

Have you ever heard of the concept of extensionality in math?

Yeah, I think it means that two functions are the same if they give the same results for the same inputs.

Exactly! It's fascinating how it applies to sets too, right?

For sure! It really simplifies things when you think about equality that way.

Synonyms & Antonyms

Root Explanation

Extensionality → It is formed from "ex-" (meaning out) and "tensio" (from Latin, meaning to stretch). The term refers to the property of being able to extend or stretch out, particularly in the context of sets in mathematics, where it describes the idea that two sets are equal if they have the same elements.

Memory Tip

Think of 'stretching out' ('tensio') to remember that 'extensionality' refers to the property of sets being equal based on their elements.

Visually Confused Words