# Why does it make sense to define 0 as 1?

## Why does it make sense to define 0 as 1?

The Definition of a Zero Factorial This still counts as a way of arranging it, so by definition, a zero factorial is equal to one, just as 1! is equal to one because there is only a single possible arrangement of this data set.

Why is a division by zero undefined?

Again, any number multiplied by 0 is 0 and so this time every number solves the equation instead of there being a single number that can be taken as the value of 00. In general, a single value can’t be assigned to a fraction where the denominator is 0 so the value remains undefined.

### Why does any number with 0 power equals 1?

On one hand, any other number to the power of 0 is 1 (that’s the Zero Exponent Property ). On the other hand, 0 to the power of anything else is 0 , because no matter how many times you multiply nothing by nothing, you still have nothing. Let’s use one of the other properties of exponents to solve the dilemma:

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Why 1 divided by 0 is undefined?

In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form.

#### Why does zero factorial equal one?

The first reason for why zero factorial is equal to one is because this is what it the definition says it should be, which is a mathematically correct explanation if not a somewhat unsatisfying one.

Why is the log of 1 equal to 0?

log 1 = 0means that the logarithm of 1 is always zero, no matter what the base of the logarithm is. This is because any number raised to 0 equals 1. Therefore, ln 1 = 0also. All the rest of the logarithmic rules are useful for solving complex equations, or equations with unknowns.