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
How can Cyclic groups be infinite - Mathematics Stack Exchange I am a little confused about how a cyclic group can be infinite To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition You can never make any negative numbers with
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
How was Zenos paradox solved using the limits of infinite series? You could just as easily argue that the sum of the distance is infinite so the distance will be infinitely far away Both statements are paradoxes But the concept of the limit of an infinite series being finite despite having infinite summands resolve both of these
Koch snowflake paradox: finite area, but infinite perimeter The Koch snowflake has finite area, but infinite perimeter, right? So if we make this snowflake have some thickness (like a cake or something), then it appears that you can fill it with paint like
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
how to prove uncountable infinite pigeonhole principle? 1 Can it be proven using the pigeonhole principle that if set A is an uncountable family of finite sets, it contains an uncountable subfamily all of whose elements have cardinality n? The idea is borrowed from here What is the Infinite Pigeonhole Principle?