Prove that a/b + c/d = (ad + bc)/bd the rule for adding fractions (ILIEKMATHPHYSICS)

[@geostorm8192]

Very cool! I have one question though, how do we define what a set is? Sure, we can say they're a collection of elements, but what does that mean mathematically? I can go "Suppose S = {1}, T = {1}", but does that mean that the element 1 is in two "boxes"? I don't like this analogy. Also, one can define "S_x = {1, x}; x≠1 and S = {S_x forall x in R-{1}}", creating uncountably infinte sets with the number one

[@carlgauss1702]

You can go crazy trying to be rigorous.

[@Dr_Owl]

Using the empty set axiom
Every other set is created by it
Like even the set {1}
Is actually { {∅,{∅}} }
So you only use the axiom the {∅} and ∅ exists

[@carlgauss1702]

@@Dr_Owl Thanks for the contribution

[@EmilioPagulayan-e7j]

​@@Dr_Owl that's 2, successor of 1.