Recent content by Citan Uzuki

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    Undergrad Does one need V not equal to L in order to do Cohen's forcing?

    Hi SSequence: Yes. If ##M## is a transitive model, then yes. For general models, the answer is no, see this stackexchange thread: https://math.stackexchange.com/questions/2118514/two-models-of-zfc-such-that-there-is-a-isomorphism-between-their-ordinals
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    Undergrad Does one need V not equal to L in order to do Cohen's forcing?

    No, L is not the minimal model of ZFC, it is merely the smallest transitive inner model that contains all the ordinals.
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    Undergrad Does one need V not equal to L in order to do Cohen's forcing?

    Generally, forcing starts with a countable transitive model M of ZFC. Since it is countable, M will not even be close to containing all subsets of the naturals, so it is possible to add a new generic set G to M. G will not be in the L of M[G], since L^{M[G]}=L^M \subseteq M \subset M[G], but may...
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    Challenge Intermediate Math Challenge - September 2018

    Hmm... you and I have very different intuitions about what the most insightful solution is. I would consider mentioning that column rank = row rank to be far more insightful than offering a formula for the solution, since it tells us why there is a solution in the first place. Additionally, it...
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    Challenge Intermediate Math Challenge - September 2018

    The ##w_i##'s exist because each ##v_i## is in the range of ##X##. Saying that there is some ##w## such that ##Xw=v## is simply what it means for v to be in the range of ##X##. I'm really not sure what more I can say on that point. As for ##Z##, I'm just using the fact that every linear...
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    Challenge Intermediate Math Challenge - September 2018

    I have a solution for problem 1:
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    What is mathematical induction

    Why are we reviving four year old threads?
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    Challenge Intermediate Math Challenge - August 2018

    I have a solution for problem 1:
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    Undergrad Limit of a two variable function

    All very true, but actually orthogonal to the point I was trying to make. What I was trying to get at is that if you are trying to find the limit of a rational function (or something which is effectively a rational function, since \sin (\theta) ~ \theta for small \theta) at the origin, the...
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    Undergrad Limit of a two variable function

    The one in the OP.
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    Undergrad Limit of a two variable function

    This limit does not exist. Note that the function isn't even defined on the path x=-y^2, and if you consider paths close to that path (e.g. x = -y^2 + y^4), the limit diverges to infinity.
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    Graduate A strategy better than blind chance

    Sure. Both players will almost surely be wearing at least one white hat. For i=1,2, let n_i be the position of the first white hat on player i's head. Then have player 1 point at hat n_2 and player 2 point at hat n_1. It is easy to see that both players win iff n_1 = n_2, which happens with...
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    High School How can you factorize polynomials with fourth degree terms?

    Actually it is. It factors as (a^2 + \sqrt{2}ab + b^2)(a^2 - \sqrt{2}ab + b^2)
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    Is P(A,B|C) = P(A|C) P(B|C), if P(A,B) = P(A)P(B)?

    No, this isn't true. Consider two fair coins flipped independently, let A be the event that the first coin comes up heads, B the event that the second coin comes up heads, and C be the event that at least one of the coins comes up heads. Then P(A) = P(B) = 1/2, P(A,B) = P(A)P(B) = 1/4, but...
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    How to find generators of symmetric groups

    Yep, that's it exactly!