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What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\\infty \\infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
What exactly is infinity? - Mathematics Stack Exchange It is just what you want it to be, as long as it makes sense mathematically We can talk about $+\infty$ and $-\infty$ in the extended real line, and about $\infty$ in the extended comlex plane We can talk about cardinalities of sets, or about ordinals, too The concept of "infinity", meaning "not finite" has very different and various meanings and uses in mathematics
sequences and series - What is the sum of an infinite resistor ladder . . . Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ $ Taking the limit as $\ n\rightarrow\infty\ $ (assuming it exists $\left \right ^\color {red} {\dagger}$) then shows that the resistance of the infinite ladder depicted in Figure $2
I have learned that 1 0 is infinity, why isnt it minus infinity? An infinite number? Kind of, because I can keep going around infinitely However, I never actually give away that sweet This is why people say that 1 0 "tends to" infinity - we can't really use infinity as a number, we can only imagine what we are getting closer to as we move in the direction of infinity
What does it mean Infinite dimensional normed spaces? I see what you mean, so does a normed-space being infinite means that it maps a vector space to a continous interval? If this is the case how do we have a finite normed-space?
Is there a shape with infinite area but finite perimeter? But the circumference also defines the subset with infinite area that lays "outside" (which is a conventional concept) That other "outside shape" would be an example of a finite-perimeter curve with an infinite area That sounds like cheating and playing with words