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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 . . .
@Arturo: I heartily disagree with your first sentence Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer) For all this, $0^0=1$ is extremely convenient, and I wouldn't know how to do without it In my lectures, I always tell my students that whatever their teachers said in school about $0^0$ being undefined, we
- 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?
@Swivel But 0 does equal -0 Even under IEEE-754 The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for + - ∞, overflow The intention is if you have a number whose magnitude is so small it underflows the exponent, you have no choice but to call the magnitude zero, but you can still salvage the
- 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 $\infty\times 0$ indeterminate? - Mathematics Stack Exchange
Your title says something else than "infinity times zero" It says "infinity to the zeroth power" It is also an indefinite form because $$\infty^0 = \exp (0\log \infty) $$ but $\log\infty=\infty$, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning
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