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• Post #4384045

  New: The Donald J. Trump Revocable Trust v. Capital One, N.A. (25-cv-21596) District Court, S.D. Florida https://www.courtlistener.com/docket/69853458/the-donald-j-trump-revocable-trust-v-capital-one-na/ 2013-2017 DOJ ran "Operation Choke Point" using informal pressure on banks to sever ties ("de-banking") with high-risk-for-fraud businesses like payday lenders, firearm dealers, and pornographic film producers. 2021/01/06 #Trump holds #Jan6 rally 2021/01/20 Trump leaves of...

• Post #4239594

  Cantor's claim is that the infinity of the set real numbers, |ℝ|, is larger than the infinity of the set of counting numbers, |ℕ|. If Cantor is wrong, then there must be a function 𝑓:ℕ⟶ℝ such that the set of real numbers, ℝ, is exactly the same as the image of all natural numbers under function 𝑓, 𝑓(ℕ) = { 𝑓(1), 𝑓(2), 𝑓(3), ... }. If Cantor is right, then there is no such function, 𝑓 where 𝑓(ℕ) = ℝ. Cantor's diagonal argument is, at its heart, a proof that a set of size 2^n is s...

• Post #1728984

  Take a set, 𝑥. Is it finite or infinite? Well what definition do you use? ① ∃𝑦 ∈ ω₀ 𝑥 ≈ 𝑦 ; There is a natural number, 𝑦, such that you may may map 𝑦 one-to-one onto the set 𝑥, enumerating each of its members. So 𝑥 is finite for the same reason { 1, 2, 3 } is finite. ② ¬ ∃𝑧 ∈ (On ∖ ω₀) 𝑥 ≈ 𝑧 ; There is no such infinite ordinal, 𝑧, such that you may map 𝑧 one-to-one onto the set 𝑥. So 𝑥 is finite because ω₀, the smallest infinite ordinal, cannot be mapped 1-to-1 into it. Do ① and ② say the sam...

• Post #1728983

  Begriffsschrift (1879), is one of the first manuscripts on #SymbolicLogic. As such, it literally invents a new language to describe the subjects the author, #GottlobFrege, wants to introduce. And this notation is very unlike what we see in math before or after this. So I will list some theorems adapted (by me, circa 2020) from #Frege with proper set-theoretical bounds. #SetTheory #Logic #Metamath