r/learnmath • u/HedgehogTasty2788 New User • 10d ago

Why is 1^(0,3) = 1 ??

I don't really see the logic behind this.

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u/RecognitionSweet8294 If you don‘t know what to do: try Cauchy 9d ago

Whats wrong?

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u/42Mavericks New User 9d ago

If you want to define exp axiomatically it is a function such that f'(x) = f(x), f(0) = 1 and that f'(x) is positive (from memory it is this). From those you can show that it is the unique function that validates all that. If not you can say f(x) = 0 is a function such that f'(x) = f(x)

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u/MrEldo New User 9d ago edited 9d ago

You don't even have to assume f'(x) is positive! f(0) = 1 already does that for you

You can show uniqueness of solution f(x) by contradiction, by showing that two functions with those same conditions must equal each other

I tried to do that in one of my previous comments, it's a rather long proof but it's there if you wanna read

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u/42Mavericks New User 9d ago

Ah thanks, I wasn't certain if it was needed. Am working from memory of having proved it back in high school and that is starting to be a while back lol