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- Is $0$ a natural number? - Mathematics Stack Exchange
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered i
- algebra precalculus - Zero to the zero power – is $0^0=1 . . .
$0^0=999$ would be a contradiction to the power laws, because then $ (0^0)^2 = 999^2 \ne 0^ {0\cdot2} = 999$ The only two values for $0^0$ consistent with the power laws are $0$ and $1$
- exponentiation - Why is $0^0$ also known as indeterminate . . .
For example, $3^0$ equals 3 3, which equals $1$, but $0^0$ "equals" 0 0, which equals any number, which is why it's indeterminate Also, 0 0 is undefined because of what I just said
- I have learned that 1 0 is infinity, why isnt it minus infinity?
Generally the only reason one sees 1 0 as infinity is because some systems (incorrectly) output infinity when given dividing by zero
- Seeking elegant proof why 0 divided by 0 does not equal 1
I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce that, based upon my assumption (which as we know was false) $0=1$ As this is clearly false and if all the steps in my proof were logically valid, the conclusion then is that my only assumption (that $\dfrac00=1$) must be false
- Zero power zero and $L^0$ norm - Mathematics Stack Exchange
This definition of the "0-norm" isn't very useful because (1) it doesn't satisfy the properties of a norm and (2) $0^ {0}$ is conventionally defined to be 1
- Justifying why 0 0 is indeterminate and 1 0 is undefined
That means that 1 0, the multiplicative inverse of 0 does not exist 0 multiplied by the multiplicative inverse of 0 does not make any sense and is undefined Therefore both 1 0 and 0 0 are undefined
- Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack Exchange
Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined
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