Why do the professional mathematicians believe blindly in so meaningless concepts as Infinity? [closed]

Question

To refute such a concept as Infinity (or many infinities) in mathematics doesn't at all require all that big efforts mainly from its own definition in mathematics.

To explain this very simple fiction in human minds, just consider the natural numbers, where simply they are a continuous chain of "endless" successive integers with no existing largest integer, where this only invalidates strictly the concept of infinity since the later is not any number nor anything else (from its own definition), so how can we truly compare it with numbers? wonder!

So, the so obvious fact of natural numbers being actually "endless" is much stronger term than using any meaningless concept as Infinity, where this concept is just a plain hopeless try to finite the natural numbers fact in order to justify and legalize so many theorems and well- established results in modern mathematics as an agreement and never any real true discovery

Why do I add this question here, because of I found no tolerance at all to all my topics that had been added in many mathematical sections, where simply the trend is always deleting my content without being able to refute me in this very basic issue,

However, many of my proven topics were including true discoveries and so many mathematical challenges that are still standing evidence where simply no one could ever bring a single counterexample (especially in Number theory and Geometry)

And to give a brief idea about those many deleted topics that the reader would simply laugh at when hearing for the first time due to huge incorrect mathematical concepts that had been built and were well-established (based on so naive conclusions or merely were just plain wrong decisions, and not at all any true proved discovery)

However, the science of physics was the main victim of the current and alleged modern mathematical sciences, where also the world economy and intelligent people waste may be regarded as the second victim of so much wrong modern mathematics

In short, I claim (with many public published so rigorous proofs) at sci.math or Quora or at SE-(here-few still undeleted topics), The following famous fallacies:

1) Imaginary numbers were simply and WRONGLY DECIDED and never were any true discovery

2) Infinity concept is a totally fictional concept that doesn't mean anything but was just introduced or fabricated to legalize so many illegal mathematics

https://www.quora.com/How-can-a-school-student-or-a-layperson-prove-rigorously-that-1-0-but-only-and-strictly-by-using-the-infinity-concept-in-mathematics/answer/Bassam-Karzeddin-1

3) The fundamental theorem of algebra totally flawed

4) The CONVERGENCE principle is also a flawed concept since the Infinite sum never exists because basically, natural numbers are endless

And if you look more carefully about the divergence or convergence you would certainly find them as the same but with so tinny deference which is that decimal notation denoted by a dot point (.), where it is not any fundamental operation in mathematics or any magical tool that can suddenly and turn the non-numbers to real numbers for sure

And the easiest way for a clever school student or a layperson to understand the deepest theme is to work for a few minutes in fractions and without using that mind blocking notation (decimal point), for sure

https://www.quora.com/When-shall-mathematicians-realize-that-no-existing-theorem-in-mathematics-would-yield-exactly-the-cube-root-of-any-prime-number

5) All real numbers associated with the fictional concept of Infinity such as the non-constructible irrational numbers (real algebraic and trans.) numbers that don't exist on the real number line (but only notations in minds), with so special story of $\pi$

See here in the below link, how is it too elementary to refute the most famous human mind fallacy in mathematics about? $$1 = 0.999...$$ where thence applicable on every alleged real number that is generally assumed with an infinite number of digits after the decimal notation, despite so many alleged proofs for this refuted fallacy https://groups.google.com/forum/#!topic/sci.math/v88rBgVXFrY

6) The impossibility of solving the general polynomials by radicals for degrees higher than fourth was so simple and so naive and beyond one's common beliefs in our modern mathematics

7) A very famous challenging example of the non-existence of many integer degrees angles of the form ($3n +/- 1$), in any existing triangle with exactly known and constructible sides, where this so obvious fact reveals strictly all the legendary real numbers in our current modern mathematics

Ref: https://www.quora.com/Do-most-of-the-named-angles-in-mathematics-truly-exist

Of course, one must consider that no Journal or University would accept such closed topics nowadays, therefore It was my duty to make them publically available to keen researchers in future, where absolute facts must be raised above all common fallacies ultimately

For interested philosophers or logicians in those many critical issues in mathematics nowadays, people can simply read many relevant topics in a free spoken site, where simply no professional control on the content of any topic, a reader must distinguish himself the facts from illusions, and not personalizing any self-issue, here: https://groups.google.com/forum/#!forum/sci.math

Note that, if all my deleted questions or answers were recovered at SE, then it would certainly facilitate the so easy task to understand all those many fictions in our modern mathematics, sure

Answer 1

I think you have some fundamental misunderstandings about how the discipline of mathematics operates.

Infinity concept is a totally fictional concept that doesn't mean anything but was just introduced or fabricated to legalize so many illegal mathematics.

Yes, "infinity" is a "totally fictional concept", but so are concepts like "addition", the idea of "less" or "more", negative numbers, fractions and decimals, imaginary numbers, even the concepts of numbers themselves.

Mathematics admits that it simply "makes up stuff" all the time. The questions within mathematics are more likely to take the form:

• Is (new idea) consistent with prior concepts, or does it contradict them in some way?
• Is (new idea) consistent within itself, or does it self-contradict somehow?
• Is it interesting (either to mathematicians, or to people in other disciplines)?
• Is it useful, either internally within mathematics (it makes some calculations easier or something like that), or useful externally (in that it appears in some way to correspond to something in the real world)?

Fractions are useful because it helps us describe how much is left of a partially-eaten pizza. Negative numbers are useful because it helps us understand a "balance" vs a "debt" in business. Calculus is useful because it helps engineers calculate an airliner's or spacecraft's trajectory. Other areas of mathematics may or may not have direct real-world applications, but might still be "interesting" to mathematicians.

Here's (one of several possible) mathematical definitions of an "infinite set":

an infinite set is a set that is not a finite set

Hmm, not so helpful without further context. So what is a finite set?

a set S is called finite if there exists a bijection (a 1-to-1 correspondence) between the set S and the natural numbers {1,...,n}, for some natural number n.

In other words, if you can "count" a set up to a specific number n, then its finite. If you can't, its infinite. (One immediate results is that the set of natural numbers itself is infinite, since there is no largest number n).

You're certainly welcome to think that this definition is strange or confusing or useless or just silly, but it does satisfy all the needs within mathematics: it turns out to be consistent, useful, and interesting (at least to mathematicians).

Note that we can even have areas of mathematics that are not consistent with each other, as long as they are consistent within themselves. Best example I can think of is Euclidean vs non-euclidean geometries. Both are useful, in different ways.

Answer 2

They do not "believe blindly in so meaningless concepts as Infinity." They actually approach the concept of infinity with eyes wide open, aware of all of the difficulties and complications therein.

A mathematician should consider it well within your right to assert that you do not consider these concepts that you describe to be "real." The finitists are a group that do exactly that. However, you should not believe that there is no infinity blindly. You should do your research to understand what sorts of conceptual issues are resolved by the concept of infinity, such as Zeno's paradox.

Mathematicians do not blindly believe in infinity. They came up to the concept from a different angle. They had models of how the world works (natural numbers, real numbers, etc), and they ran into issues where these concepts did not line up with reality. Zeno's paradox, which I mentioned earlier, is one of the easy ones which makes the argument that you can't move anywhere. As mathematicians can obviously see that we appear to move places, they needed to update their models. So they put out concepts which would help make their models function, and tested them thoughtfully. Infinity is one of the concepts which has by and large survived the testing.

Myself, I recommend reading up on what infinity actually means to mathematicians, with an open mind. For example, your wording seems to suggest that you think mathematicians consider "infinity" to be a number. For much of mathematics it is not a number. It is a cardinality. It is a measure of the size of the set of natural numbers. There are areas of mathematics where you do see infinity as a number (transfinite/ordinal numbers) and they take great care to treat it differently from the cardinality concepts. Much of mathematics does not depend on these transfinite concepts. Mathematicians will still generally give credit to them, because the concept is rigorously defined and consistent, but that doesn't imply that they must believe in them as anything more than an intellectual concept. The concept of infinity as a cardinality has much wider acceptance because has been found to lead to useful real world implications (such as calculus, which got us to the moon).

I won't explore your other questions, because stack exchange format prefers to focus on one question at a time, but the argument is the same for all of them: mathematicians did not believe in them blindly. They defined them and carefully analyzed to make sure they seemed reasonable.

If you are interested, I recommend the VSauce video How to Count Past Infinity. It captures the concept well without assuming you have a substantial math background. And he also is willing to dig at the question you are asking without dismissing it outright. (it's roughly 13 minutes in, but I don't recommend skipping. let him make his argument first)

You may also be interested in researching the Axiom of Choice (AoC). It's a funny little axiom which looks benign, but leads to all sorts of funny issues such as the Banach-Tarski paradox. It is an example of a modern day abstract concept which is in the process of being accepted or rejected by the mathematical community, so it's a great way to shed light on how they go about accepting or rejecting these things with eyes wide open.