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 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?
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
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
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
linear algebra - Is there a quick proof as to why the vector space of . . . Your further question in the comments, whether a vector space over $\mathbb {Q}$ is finite dimensional if and only if the set of vectors is countable, has a negative answer If the vector space is finite dimensional, then it is a countable set; but there are infinite-dimensional vector spaces over $\mathbb {Q}$ that are countable as sets
Circle whose radius is infinite - Mathematics Stack Exchange I have the intuition that a circle whose radius is infinite is a straight line Nonetheless, I don’t feel that what I’ve just stated is really scientific as it has some vagueness and lacks precisi