It won't since your language is a computer based language, you can only involve numbers or characters.Not sure. For example, if there is a rewrite rule "x/0 = ∞" for x not zero, the symbol could start popping up in output expressions. If you feed that output expression into your function F(x), it depends on whether F will accept it as an argument, and if so, if can successfully associate an output to it. Not sure at all.
Whether you want to replace --> with =, they are relations and quantification over infinite terms does not makes sense. That's my point.rewrite rule: ab-->cd
I understand that cryptography requires an abelaian group for keeping all values of operations under the group but l can assure you the point at infinity is not related to infinity we are discussing here. There is no operation in solving weierstrass equations which involves the infinity symbol.It is just an example of an algebraic structure in which adding a concept of infinity keeps the entire system consistent. Otherwise, the domain has no identity element, and then is no longer a group.
Finitist mathematics is not meant to discount the standard mathematics, we are just exploring a new world which is limited. Theory is more important than applicationTherefore, it is a bit late in the game to argue whether extending a domain with the infinity symbol makes sense.
Whether you want to replace --> with =, they are relations and quantification over infinite terms does not makes sense. That's my point. — Wittgenstein
Finitist mathematics is not meant to discount the standard mathematics, we are just exploring a new world which is limited. — Wittgenstein
What is the standard definition of number ? — Wittgenstein
The cryptography technique using weierstrass equations that you mentioned uses finite field , like galois field.Galois fields? Pick a prime power p^n and carry out all arithmetic modulo p^n. Approximately all algebraic structure that exists over infinite/countable will turn out undamaged!
I think it is possible to use an infinite field but more difficult than a finite field. — Wittgenstein
How about having a matrice A.X=Y where A,X and Y have infinite number of rows and columns,X is the solution set which contains the secret, a row or a column in the matrix can specify the operations to perform on A to obtain A inverse. — Wittgenstein
This sounds really naive and stupid but l hope you can suggest improvements to using matrices in cryptography. — Wittgenstein
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