Math Memes

The "=" symbol defines an equivalence relation. So "1+1=2" is one definition of "2", defining it as equivalent to the addition of 2 identical unit values.

2*1 also defines 2. As does any even quantity divided by half it's value. 2 is also the successor to 1 (and predecessor to 3), if you base your system on counting (or anti-counting).

The youtuber Vihart has a video that whimsically explores the idea that numbers and operations can be looked at in different ways.

Using the Peano axioms, which are often used as the basis for arithmetic, you first define a successor function, often denoted as •' and the number 1. The natural numbers (including 0) then are defined by repeated application of the successor function (you also first need to define what equality is):

0 = 0 1 := 0' 2 := 1' = 0'' etc

Addition, denoted by •+• , is then recursively defined via

a + 0 = a a + b' = (a+b)'

which quickly gives you that 1+1=2. But that requires you to thake these axioms for granted. Mathematicians proved it with fewer assumptions, but the proof got a tad verbose

That assumes that 1 and 1 are the same thing. That they’re units which can be added/aggregated. And when they are that they always equal a singular value. And that value is 2.

It’s obvious but the proof isn’t about stating the obvious. It’s about making clear what are concrete rules in the symbolism/language of math I believe.