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75 points measurablefunc | 1 comments | | HN request time: 0s | source
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jbandela1 ◴[] No.46177607[source]
I think the biggest mistake people make when thinking about mathematics is that it is fundamentally about numbers.

It’s not.

Mathematics is fundamentally about relations. Even numbers are just a type of relation (see Peano numbers).

It gives us a formal and well-studied way to find, describe, and reason about relation.

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1. gerdesj ◴[] No.46178296[source]
To form or even to define a relation you need some sort of entity to have a relation with.

My wife would have probably gone postal (angry-mad) if I had tried to form an improper relationship with her. It turns out that I needed a concept of woman, girlfriend and man, boyfriend and then navigate the complexities involved to invoke a wedding to turn the dis-joint sets of {woman} and {man} to form the set of {married couple}. It also turns out that a ring can invoke a wedding on its own but in many cases, it also requires way more complexity.

You might start off with much a simpler case, with an entity called a number. How you define that thing is up to you.

I might hazard that maths is about entities and relationships. If you don't have have a notion of "thingie" you can't make it "relate" to another "thingie"

It's turtles all the way down and cows are spherical.