is there any empirical evidence that x(y + z) = xy + yz? if not, then how do we know that it's true?

# Is there any empirical evidence that x(y + z) = xy + yz? if not, then how do we...

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You can test it as much as you like with different numbers, so yeah, there is empirical evidence. Proofs is still better though.

Well it depends on how you use distribution

if you try and find evidence in a system that uses such mathematical structure that doesn't allow for distribution than you will not be able to find any evidence. If you however use it in a structure that does allow, you will find plenty

Maths is just an abstraction anyways, you don't need empirical evidence for something to be true. Distribution is true because we define it that way. 1+1 = 1 is true if I define it + that way in a mathematical structure, it is true because I say so. And bonus, I can find empirical evidence

a rain drop + a rain drop = a rain drop

1+1 = 1

empirically proven

Learn algebra you fucking twat

**wolframalpha.com**

Output from a closed source CAS is not an argument.

i am a mathematics major and have learned math, just why should i take it at face value that x(z + y) = xd + zy? how could we possibility know that without having a repeatable experiment that demonstrates the result?

i am a mathematics major

no you're not

How can we know that x(z + y) = xd + zy ?

Because we defined multiplication and addition that way

doesn't know the difference between a definition and a theorem

Sure you're a math major

LEARN ALGEBRA YOU WANKER

how could we possibility know that without having a repeatable experiment that demonstrates the result?

i am a mathematics major

If you really were, you wouldn't be asking this question