0!=1 PROOF | Zero Factorial is Equal to One

Let x be real number. Observe that a^x/a^x=1. By laws of exponent a^x/a^x=a^(x-x)=a^0=1. Hence Proved.

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In certain areas of mathematics, such as combinatorics and algebra, 00 is conventionally defined as 1 because this assignment simplifies many formulas and ...

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a0 means multiply by a 0 times. Since we aren't multiplying at all, we get the multiplicative identity, 1 (anything times 1 is itself).

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In this last case, "a0=1" is a definition, but it is also the only sensible one given the meaning of a1,a−1,a2,a−2,a3,a−3, etc. Benjamin Dickman.

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Any number divided by itself is 1, x 0 =1. 1 is, in a sense, to multiplication what 0 is to addition. They're the identity element , meaning x* 1=x and x+0=x.

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So for a^0 we divide a¹ by a , we get a/a which is 1. Therefore a^0 is always 1. Upvote ·.

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