
Post by Eugene 2.0 on Nov 17, 2020 17:32:09 GMT
Let's take a random variable a (in math). We can say either it's monomial, or polynomial, i.e. either it is a number (or a group of it), or another variable (or a group of it).
But here's a question: is it true that behind each variable in Math there is a number or a group of numbers? (The same question written symbolically):
(∀y)(∃x){[(Vy≡"y is variable") & (V_{1}y≡Vy ∨ V_{2}y≡Vy ∨ ... ∨ V_{n}y≡Vy)] ⊃ [(Nx≡"n is number") & (N_{1}x≡Vy ∨ N_{2}x≡Vy ∨ ... ∨ N_{k}x≡Vy)]}
(another way):
(∀a)(∃x)(a≡x ⊃ x ∈ ℔) (where "℔" is a symbol of any number; i.e. it might belong to rational, or natural, etc.)
Or is it possible that some variables don't have numbers behind them, and if there are, what are these variables?



Post by archlogician on Dec 15, 2020 15:27:41 GMT
I am struggling to parse your question. At a naive reading, mathematicians certainly make use of variables ranging over sets, functions, etc. If you mean this in some sort of Godellian arithmetisation of syntax sense, then I would really suggest the book "Axiomatic Theories of Truth" by Halbach as very illuminating as to the technical details of working with such systems?



Post by Eugene 2.0 on Mar 11, 2021 18:33:09 GMT
I am struggling to parse your question. At a naive reading, mathematicians certainly make use of variables ranging over sets, functions, etc. If you mean this in some sort of Godellian arithmetisation of syntax sense, then I would really suggest the book "Axiomatic Theories of Truth" by Halbach as very illuminating as to the technical details of working with such systems? I really appreciate your comment. Not being a mathematician for me many terms are out of understanding it precisely. Usually I ask as more plain as possible questions. This questions is that: do math operates values only or there are other deities [not valuable] it can operates the same way? Thank you for advising a book.

