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
probability - Given an infinite number of monkeys and an infinite . . . Just get an infinite number of monkeys (or a slightly smaller number of computers) and opening a publishing business Make a million bucks and retire But this rings false, especially since modern computing power (relative to the difficulty of the task) is practically infinite, putting the practice of this philosophy within reach
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?
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
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