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I am intrigues by mathematical facts that are very easy to know to be true instinctually or with a verbal explanation but are very difficult to write proofs for.

A good example of this is the four color theorem.

@freemo

a^0=1

The most basic of exponents. But I am sure, a lot of people can't prove it.

@zevahs Its axiomatic not provable. We choose that particular convention simply because it is useful and ensures consistency with other patterns. See the exponent is a defined operator in principle we could define its behavior however we like, it just wont be too useful if we do.

@freemo
I thought it was provable?
Suppose,

a^x/a^x=1

By the property of exponents we know x^a/x^b = x^(a-b)

Applying that,

a^(x-x) = 1
or, a^0 = 1
@zevahs

@shibaprasad
Yes but my point is the property of exponents is an axiom, we define what an exponent is
@zevahs

@shibaprasad
I was wrong though in aaying it isnt provable. Only that it is provable from the axioms
@zevahs

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