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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
elementary set theory - Definition of the Infinite Cartesian Product . . . The depth of the tuple scales with the number of terms in the product; infinite caretsian products lead to infinite descending chains The two sets you give are infinite descending total orders, but what ZFC forbids is infinite descending chains for the elementhood relation, which would arise as I note above for infinite cartesian products
One divided by Infinity? - Mathematics Stack Exchange Infinite decimals are introduced very loosely in secondary education and the subtleties are not always fully grasped until arriving at university By the way, there is a group of very strict Mathematicians who find it very difficult to accept the manipulation of infinite quantities in any way
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
What is the difference between infinite and transfinite? The reason being, especially in the non-standard analysis case, that "infinite number" is sort of awkward and can make people think about ∞ ∞ or infinite cardinals somehow, which may be giving the wrong impression But "transfinite number" sends, to me, a somewhat clearer message that there is a particular context in which the term takes place
De Morgans law on infinite unions and intersections Then prove that it holds for an index set of size n + 1 n + 1 and wrap it up by n → ∞ n → ∞ but I'm not convinced that's right For example, an argument like that doesn't work for countable intersection being closed on a collection of open sets So what's a good proof that can extend de Morgan's law to an infinite collection of sets
Examples of Infinite Simple Groups - Mathematics Stack Exchange I would like a list of infinite simple groups I am only aware of A∞ A ∞ Any example is welcome, but I'm particularly interested in examples of infinite fields and values of n n such that PSLn(F) P S L n (F) is simple References about this topic, or any example, are also appreciated