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- 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?
- 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
- Can a countable set contain uncountably many infinite subsets such that . . .
Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
- Is it viable to ask in an infinite set about the Cardinality?
Can you ask given an infinite set about its cardinality? Does an infinite set have a cardinality? So, for example, what would be the cardinality of $+\\infty$?
- 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
- 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
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