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    Thanks for the clarification @holtzermann17 .
    Christian N. Hofmann
    i need a proof of catalan's identity
    Christian N. Hofmann
    found it by myself. bye
    Joe Corneli
    @ch180 - first link by googling "planetmath catalan's identity". Good luck!
    Joe Corneli
    Looks like Native MathML plugin is working now \square.
    how to do request?

    Hi there,
    I am looking for a faster algorithm for counting the number of data points that are close to a particular point in k-dimensional hyperspace? The current method of calculating all the distances to data points is too slow for my application to handle.

    (If this should be posted elsewhere then please let me know)
    Thanks in advance

    @holtzermann17 Is the data for planetphysics available somewhere?
    Tarit Goswami
    Hi, I am new here, can I know what does it mean by well defined ?
    transfer function
    Can anyone help me with an issue about Scott-continuity?
    This is what I'm trying to solve; if you could give me any hints I'd be grateful
    @eachirei -- probably not the best forum for questions like this; see math.stackoverflow. Also, posting homework questions and providing no context of what you've attempted is unlikely to trigger someone to explain the answer.
    How to look up an article in PlanetMath? I am looking for the article "http://planetmath.org/APointAndACompactSetInAHausdorffSpaceHaveDisjointOpenNeighborhoods"
    The link doesn't work; it takes me to the home page for PlanetMath rather than the article
    Hi there , nice to meet you all
    Joe Corneli
    @genenaden indeed, that page seems to be missing for some reason. At some point we might be able to track it down.
    how does this chat room work?
    Anyone here?
    Can you guys help me with a proof?
    Nabeegh Ahmed
    @nunesgrf yes??
    Favour Otiger
    Hey guys
    hello, do you guys have links or popular resources for engineering math?
    hopefully open, and free :)
    good day party people
    I'm proofing my way through tao mostly sloppily and im considerung posting my so-called proofs here
    id this hinders chat from pulsating tell me and ill stop,, wont be much anyways
    (e) Let X and Y be finite sets. Then Cartesian product X ×Y is finite and #(X × Y) = #(X) × #(Y).
    i'll try with induction over #Y
    For #Y = 0 the cartesian product is the empty set and the proposition is trivially true.
    So We know #(X1×Y1) = #X1 ⋅ #Y1
    We try to prove #(X2×Y2) = #X2 ⋅ #Y2 for #Y2 = #Y1++
    Let's choose an arbitrary element a2 from Y2 then #(Y2 \ {a2}) = #Y1
    X2×Y2 = X2×(Y2{a2}) ∪ X2×{a2}
    as both sets are disjoint #(X2×Y2) = #(X2×(Y2{a2})) + #(X2 × {a2})
    and #(X2×(Y2{a2})) = #(X1×Y1{a2})
    j: X2 → X2 ×{a2} = j(x) = (x, a2) for x in X2 is a bijection
    so #(X2×{a2}) = #X2
    and #(X2×Y2) = #(X2×(Y2{a2})) + #(X2×{a2}) = #(X1×Y1) + #X1 =
    = #X1⋅#Y1 + #X1 = #X1⋅#Y1++ = #X2⋅#Y2
    i think illl rater spam my stuff in some forum
    Im in calc 2 anyone think they can give me a hand?
    Victor Porton
    I discovered algebraic general topology and a generalization of limit for arbitrary functions: https://mathematics21.org - congratulate me
    Victor Porton
    will submit to PlanetMath
    is the sum of two normally distributed random variable X and Y alwways norma
    is the sum of two normal variable always normal??
    Rana Zubair
    can someone please explain to me what is inverse CDF function. It will be really appreciated, i could not get any clear understanding of it.
    Kedar Mhaswade

    Hello! It's my first time here. Please be kind!
    First off, thank you for a monumental effort. It's almost like Bourbaki reincarnated for the masses!

    Is there a Makefile on the planetmath repo to create the true local copy of planetmath with cross-linking sections, indexed items etc.?

    any metrizable space is second countable
    Tejas Shetty

    I discovered algebraic general topology and a generalization of limit for arbitrary functions: https://mathematics21.org - congratulate me


    Hello, could you please explain me channelized Hotelling observer?
    How do I report an error? I believe there is an error in the entry https://planetmath.org/complementarysubspace I originally I have my argument typed up in MathJax, but don't know how to submit it.