Recent content by Numberphile

  1. N

    Topological Basis Homework: If-Then Conditions

    Homework Statement Let (χ,τ) be a topological space and β be a collection of subsets of χ. Then β is a basis for τ if and only if: 1. β ⊂ τ 2. for each set U in τ and point p in U there is a set V in β such that p ∈ V ⊂ U. 2. Relevant definitions Let τ be a topology on a set χ and let β ⊂ τ...
  2. N

    Elements of an Equivalence Class

    Ah, I see it now! (Though I think the signs are a bit off, but nonetheless it should be the same) Since 25xy + 5xl + 5yk = 5(5xy) + 5(xl) + 5(yk) = 5[5xy + xl +yk], then this is just an 5z, as [5xy + xl + yk] is just some integer. Perfect! Thank you so much.
  3. N

    Elements of an Equivalence Class

    I'm not sure that I follow the logic. mn - kl = (5x+k)(5y+l) - kl I expanded this, and trivially, I obtain that mn - kl = mn - kl
  4. N

    Elements of an Equivalence Class

    I may have made a mistake in my "What I've tried" section. I already corrected it in my original post. It should have read My apologies.
  5. N

    Elements of an Equivalence Class

    I haven't calculated that because I'm not sure what that would represent. I know an equivalence class is defined as a relation on a set S with x ∈ S, then the equivalence class of x is Ex = {y ∈ S | x ~ y}
  6. N

    Elements of an Equivalence Class

    < Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Question: Let ~ be the equivalence relation on the set ℤ of integers defined by a~b if a-b is divisible by 5. Let k ∈ Em belong to the equivalence class of m, and l ∈ En belong to the equivalence...