What is a number?

some do, not many. I recommend Tao's Analysis I, it's great for this kind of thing

fuck off

>describe fenomena
they do not. scientists do not describe anything but the numerical outputs of some tools that they bought from somebody else. Scientists do not rely on their 5 senses, they are not empiricists. Scientists claim that their imagination is a way to ''truth'' or ''objectivity'' or some other big words that somehow describe a' ''reality'' wherein humans are not, and of course to sort all their fantasies, since they think that senses are shit and corruptible, they build the fantasy of ''validity'' of a fantasy with respect to something that ''is not human''.
at this point, the rationalists can either go even more full retard by clinging to a sky daddy, or can go full retard like ''nature'' but of course there is no ''nature''. There is what is experiences thru the 5 senses and what is experience through the imagination [= opinions, ideas, through, concepts, inferences, whatever]. So some guy though he was genius because he slapped back his fantasies against ''the 5 senses'' as the validity of inferences, to check whether his ''inferences'' were valid.

but it turns out that what is experienced through the senses is just what is experiences through the senses, no matter how hard people cling to their fantasy of a validity of a ralitionalism-claiming-to-be-empirisist. Well the only good thing from this religion by the secular humanist is that it has been providing, for the last 300 years, a salary for lots of people in the liberal revival of the academia

Mathematics is nothing more than a concretization of the organizing principles of reality, in much the same way that language is a concretization of the contents of reality. Does the word "the" seem any more mysterious to you than the number one?

so the trick of those people is to develop ''models'' (modelling what? nobody knows) and then to make the model compete and say ''this model is more valid than this model''.
Of course a model cannot model the ''reality'' since to model the reality you must know the ''model of the reality'', plus the ''reality'' plus the comparison between the ''model of the reality'' with the ''reality''.
But if you know the ''reality'' you do not care about modelling it in the first place.

Then they develop statistics, because those people claim that statics somehow gives you ''truth'' and the other big words that they love. Of course they have no proof of this, for people who love to claim they prove things it is disappointing from them.... THey claim that you cannot know knowledge with ''just one event''.
They claim that their fantasy of the ''repeatability of the conditions leading to an effect'' is the way to check ''a model against the reality'' (which is again retarded).

So how do you get truth from stats according to these people. You run your little model, you run an ''repeatable experiment'' several times (these people love to claim that the condition producing an event are stable across time) and you collect ''data'' which is ''the reality'' (these people love to claim that reality is just a bunch of numbers,like a photon, and then those numbers are axiomatized, by those people, as some sets).
After this you read a book, where the ''convention'' for determining ''the truth'' is to have a statistical significance. So for instance people in biology claim that ''the statistical significance'' for some ''repeatable experiment'' is ''3 sigma'' or some ''p value of whatever number they choose at this date of the conference''.

then they publish their articles, they are happy about what they are doing, they get their salary and a few awards if people have faith in their article and they die. This is their rewards.

>why is it 0 + a = a
>why is 1*a= a

Are you serious user, or are you trying to seem thoughtful?

Let me explain how addition with natural numbers works:
Zero is nothing or lack of
Z is the quantity of things which can be counted as separate objects. That is, they're distinct

0 + z = z because if we have z quantity of apples in a basket and add 0 apples (or nothing), we still have z apples.

And why 1* a = a
Multiplication is a way to quicken addition. 1*a means we have 1 quantity of a. 2*a means we have 2 quantities of a, and so forth. Well, if we have 1 quantity of a, then we just have a. If we have 2 quantities of a, we have a+a, etc.

We can sub out for a and have it now represent a quantity itself, and so on, and so forth

this is such a terrible post, with info taught to 8 year olds, misunderstanding the question completely, and still you manage to come off as super condescending
stop posting

You're a pseudo-intellectual who's upset I gave him the juvenile answer his inane question deserved.

And just for the record - that was a proof by example, bruh

If I had shown you the literal basket there would've been no question as to whether or not it was true, as I had specifically defined zero to be the quantity of nothing.

This sounds depressing. Is there no absolution for a model that goes beyond formalism empiricism and intuitionism.

Thats just repeating the question to me. I want to know why 0 apples can exist in a set of apples and can be added. Can you hold 0 apples? Can you taste 0 apples? Then why is it still in the set?

>…gives you "truth" and the other big words that they love…
>…"truth" and the other big words…
Really makes you think

this is the worst possible way to explain this.

It exists because it's a convienent way to describe the world and that's how we have defined it. Our basic mathematical truths are provable in the real world because they describe real phenomena.

Anyway, since you seem to be hinting at sets, here is the axiom of the empty set:

en.m.wikipedia.org/wiki/Axiom_of_empty_set

Where the simplest numbers, natural numbers are concerned, a really important part of /number/ as-such is the notion of a bijection.

There are two cows in a field, a Holstein, and a Guernsey. There are two fruits on the picnic table near their grazing area - an apple, and a kiwi.

Why is it that each of these collections of things can have the label /two/ appended to them? What is it that they have in /common/, that they (the pairs) are each "/two/"? This is where you're getting at what number actually is, and thinking about it with some depth.

In each case, you can pick something out of each collection, and "assign" it to something in the other collection, so that everything in one collection gets associated with just one other thing in the other collection, and with nothing left over in either collection. These two things, put together, define what a /bijection/ is, which is just a special type of mapping, or function, or more simply: a rule for assigning things in one collection to other things in another collection.

The number, then, in the natural case anyway, is exactly this same possibility of mapping between sets - for each number.

This concept of bijection unperpins our concept of number itself, at least where counting is concerned (as opposed to measuring, comparing lengths, etc). It's so fundamental that it can be extended to infinite sets, in order to compare them (this is why mathematicians say that certain infinite sets are "bigger" than others, though to a neophyte this seems to be a senseless statement). If there's stuff left over in an infinite set, or rather, if no bijection exists between two infinite sets, then the set with stuff left over is said to be some version of "bigger".

If you want to know what a number is go back to preschool, brainlet

Only prime numbers exist. The other numbers are just made out of primes. 0 is not a number.
Prove me wrong. I bet you cant.