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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.
@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
@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