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- 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?
- 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
- linear algebra - What can be said about the dual space of an infinite . . .
The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions This was discussed on MO but I can't find the thread
- 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
- real analysis - Why set of natural numbers is infinite, while each . . .
In his book Analysis Vol 1, author Terence Tao argues that while each natural number is finite, the set of natural numbers is infinite (though has not defined what infinite means yet) Using Peano
- abstract algebra - Examples of infinite groups such that all their . . .
I am in need of examples of infinite groups such that all their respective elements are of finite order
- 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
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