A simple question but care is needed for a mathematically consistent answer. See Preprint The Countable-Infinity Contradiction
The largest value of finte is as large as you want provided it is not infinite. What is the largest natural number? It is as large as you want provided it is not infinite. To describe the set {1,2,3,...} as infinite and complete is mathematically inconsistent. This set by definition is as large as the largest natural number, which is finite. Finite and unbounded are potential infinities, required by mathematical consistency to always remain in an incomplete state. Unbounded mathematics cannot be both consistent and complete. The axiom of infinity is inconsistent and thus forms a faulty foundation for mathematics.
The largest value of finite not exist.
A set is finite if every subset of this set is not equivalent of it. So, if exist the largest value of finite then exist a subset of natural numbers set such that if we add another natural number in it then it is infinite. So, exist a subset of it that is equivalent with this set. Thus, exist an natural number k
Enkeleda Kallushi Agreed. There is no largest value of finite in unbounded mathematics. Finite is a potential infinity, required by mathematical consistency to always be incomplete.
I think the following paper is useful
What is the Computational Value of Finite-Range Tunneling?
Denchev, Vasil S., Boixo, Sergio, Isakov, Sergei V., Ding, Nan, Babbush, Ryan, Smelyanskiy, Vadim, Martinis, John, Neven, Hartmut
https://booksc.xyz/book/60107010/26d168
As THE LARGEST VALUE of any finite one you can take any VALUE, which is FINITE. And it will be true, by definition.
Anatolij K. Prykarpatski Ageed. The same is true of the natural numbers, which is why they may not be described as infinite (and infinite set theory is inconsistent). Finite and unbounded form potential infinites. They are required by mathematical consistency to always be incomplete. To complete them is to make finite and infinite the same, which is inconsistent.
To Ed:
You, eventually, know that natural numbers, next rational numbers, as countable sets, are generalized next to real numbers, whose quantity, or its infinite set power is called alef - zero "cardinality". This procedure can be this way generalalized further to greater cardinality numbers as alef-1, alef-2 etc, and one has that 2^{alef-0}=alef-1, 2^{alef-1} etc. These numbers can be used as some measures of any infinite sets, if one wishes to compare them to each other.
Best!
Anatolij K. Prykarpatski yes, I am aware of this but it is inconsistent (so incorrect) and I would like to see it corrected. The infinite set theory concept of a power set is particularly confused and leads to the equally confused concept of cardinalities of infinity. All any of the proofs by contradiction actually show is that you can't count to infinity. See Preprint The Countable-Infinity Contradiction
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