uhm, 1st and for most, Sirs and masters, is \(\frac{k}{0}\) (where \(k\) is a constant) equal to infinity? or it is really called undefined? or both?

secondly, \(\frac{k}{infinity}\) (where \(k\) is a constant), is it equal to zero?

third and last, \(\frac{0}{0}\), is it meaningless? undefined? zero? one? infinity? or what?

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TopNewestokay, I'll try to explain.

first, about those words you say.

zero = nothing but not empty. zero is the inner gate to go to another rule of measurement.

infinity = the greatest size of everything. infinity is the outer gate to go to another rule of measurement but still can't reach until now, differ from zero which so easy to symbolize.

undefined = not yet defined. it means human not yet has word to symbol that thing.

and you just stated \(\frac{k}{0}\), but not only that constant because everything divide by zero has unlimited possibilities.

why I say "unlimited possibilites"? it because if you divide anything with nothing, then the result was so many or we called it as "infinite amount of calculated values", not the infinity one.

what's the differences between infinite amount and infinity? infinite amount is the total of the result was unlimited or too many of them to count or not yet can counted or we say it as "uncountable". infinity is the greatest value of everything, but infinity is just one number or one thing that has massive size, not too many things, but just one thing that has amazing or uncalculated size. still confuse?

next, \(\frac{k}{\infty}\), okay we already know not only that contant is it? because \(0\) and \(\infty\) (infinity) are the gate of measurement or border of measurement. let's imagine, \(\infty\) is the biggest of the biggest, it means when we say that we has value for example \(100000\) and divide it by \(\infty\), the result will be the smallest (not the smallest of the smallest) or we called it nothing or \(0\).

and your last question. \(\frac{0}{0}\). that actually same as we divide anything with zero. because nothing divide by nothing is uncountable result, it can be \(0\), it can be \(1\), it can be \(2\), it can be \(3\), it can be \(-8\), it can be \(\infty\) too, it can be anything, too many result and never successfully counted.

here what you requested:

\(\frac{k}{0}\) = \(\frac{\infty}{0}\) = error or overload or uncountable results

\(\frac{k}{\infty}\) = \(\frac{\infty}{\infty}\) except \(\frac{\infty}{\infty}\) = \(0\)

\(\frac{0}{0}\) = \(\frac{\infty}{0}\) = error or overload or uncountable results

and you miss this one.

\(\frac{\infty}{\infty}\) = undefined

infinity divide by infinity is undefined because ...

even I still can't explain that.

YIS – Yulianto Indra Setiawan · 3 years, 8 months ago

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Infinity is not a number. Its just a concept. So, I think we leave such topics undefined. But we work with infinity in limits. – Vikram Waradpande · 3 years, 8 months ago

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I found this video which explains the dividing by 0 cases really well.. – Mattias Olla · 3 years, 8 months ago

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Anything divided by zero is undefined (it doesn't make sense if you divide something by zero). Infinity isn't a number (mainly because it doesn't obey the rules of regular numbers). So mathematics doesn't evaluate anything with infinity in it. 0 divided by 0 is sometimes regarded as

indeterminate(it could be anything). – Mursalin Habib · 3 years, 8 months agoLog in to reply