For instance, in combinatorics, defining 0 0 = 1 aligns with the interpretation of choosing 0 elements from a set and simplifies polynomial and binomial expansions. However, in other …

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In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case. Using fraction notation, the general example can be written as , …

One Equals Zero! The following is a “proof” that one equals zero. Consider two non-zero numbers x and y such that. x = y. Then x 2 = xy. x 2 – y 2 = xy – y 2. x + y = y. 2 y = y. Thus 2 = 1, since …

The expand-o-tron to the rescue: 0^0 means a 0x growth for 0 seconds! Although we planned on obliterating the number, we never used the machine. No usage means new = old, and the …

In general, there is no good answer as to what 00 "should" be, so it is usually left undefined. Basically, if you consider xy as a function of two variables, then there is no limit as (x, y) → (0, …

Why some people say it's 0: Zero divided by any number is 0. Why some people say it's 1: A number divided by itself is 1. Only one of these explanations is valid, and choosing the other …

Mostly it is based on convention, when one wants to define the quantity $\binom{n}{0} = \frac{n!}{n! 0!}$ for example. An intuitive way to look at it is $n!$ counts the number of ways to …