/sci/ - Science & Math

>>15158696
The real numbers are in fact fake.

>Infinity is not finite,
Again, the ability to assert that there is a logical negation of a term i.e. finite is negated by infinite/non-finite. Does not imply the existence of a number called infinity and is not justification of such a thing. Rather paradoxes like the Russel Paradox or various other paradoxes derived from modern set theory like the Banach-Tarski paradox prove there logically cannot be objects as assuming their existence leads to blatant logical contradictions.

Finite only means that a natural number can be assigned to the quantity of objects of a certain type in this context. Infinite, being the negation implies that a finite-number cannot be assigned a natural number. The fact that there is a negation again does not imply the exist of an object called infinity. It does not imply anything like
>not constrained
>It has no end.
as you are positing. At best, it means that an additional digit or an additional element can be added
>It can't be treated like a number.
Rather there is no such thing as an object called infinity in this context. Plain and simple.
>>15113984
Absolutely. Much of modern math is a shellgame.

>>15074554
The problematic aspect of these "principles" is that many of them are founded on convenient word salads rather than intuitive and understandable notions. The people who appeal to them and invented them didn't even know what they really meant so it's not surprising that you don't understand them.

>>15058416
>you can model arithmetic with sets
It works perfectly fine for finite sets or if you're trying to defining natural numbers in terms of "m-sets." But it's unclear what's even going on with alleged infinite case. Moreso, no one can talk about arithmetic in the alleged arithmetic case. The only thing you get is some construction which is incredibly unclear as to how it relates to the idea of a number and often fails completely as a means to calculate new examples of numbers, or they depend on circular reasoning (no one has ever seen a real number so lets define the infinite sequence which we'd like to be able to find a "real" number at the end to be the "real" number). Meanwhile all the logical problems are handwaved away as these things are merely just given lip service while everyone just treats the arithmetic and existence of such numbers as an "axiom."
>you can define functions as sets.
Ordered pairs in the finite case as a definition is quite intuitive as a special finite list of pairs. However, the "definition" of a "function" as a "set" in any alleged non-finite case are quite problematic as there is no reason to imagine such a thing as a pair. The only things anyone can actually correctly talk about are finitely written expressions like [math] f(x) = x^2 +1 [/math]. However, in this case, one need not even appeal to sets it is solely: given two objects of a specified type, the expression must evaluate uniquely. The only truly tangible and hence meaningful parts of this definition are in the formal arithmetic. The "set" portion of the definition is at best lip service and not necessary. It's meaningless and does not accurately describe the reality of what is usually meant by a "function" like a polynomial or a power series. Everything about a "function" for non-finite cases is entirely in the formal arithmetic and a finitely represented expression given in terms of that arithmetic.

>>14991510
With many mathematicians it's typically them pretending to be able to do something they can't do and then some sleight of hand to pretend they actually did something meaningful when much of their work is founded on gibberish.