[talanum1 (OP)]

It is because there is no real number next to zero. However in real life: take a line on a tiled floor. We know there is molecules right next to the line and they do not tend to zero. If this wasn't so there would be no tiling of floors

[evan_au]

There are some people for whom mathematics is very intuitive. Évariste Galois was denied any mathematical education - partly because he immediately jumped to the answer, and didn't show any working (he didn't need any intermediate steps). Not helped by the fact that France was in a class war at the time, and coming from a poor family, he did not get on with the nobility in the schools, or the people running the schools for the nobility.

He invented a field of mathematics now called Galois fields, which has been used in cellphones and optical fiber networks.
https://en.wikipedia.org/wiki/%C3%89variste_Galois

[Eternal Student]

Hi.

He invented a field of mathematics now called Galois fields,

     Possibly.  He is more famous for developing "Galois theory".  He is considered to have been one of the first to write and publish a paper about Number Theory in which finite fields were used and formally described.   However, it's unlikely he was actually the first to use finite fields, just the first to get it noticed and do something usefull with it.   I don't know, I'm not an expert in the History.   

We know there is molecules right next to the line and they do not tend to zero. If this wasn't so there would be no tiling of floors

   Tiling college has it's secrets but I'm fairly sure this is what they do:  I think they learn how to use electromagnetic forces that exist between tiles.  They are able to put the tiles so close to each other that no other particles could possibly get between the tiles because the electromagnetic forces would repell them.  It's a bit of trade secret but I don't think the molecules are really in contact with each other.  If they don't have perfectly flat and straight edges on the tiles then they seem to have some kind of "continuum covering compound" (triple C or "grout") which they can use to cover the gap.
    I've never really got this work well myself but the theory seems sound.

Best Wishes.

[Deecart]

Not sure i understand well the problem you are talking about.
But it is possible we both have the same questioning.
So this is how i see that :
If you draw a line or even consider a line without drawing it, there is two ways to understand "the line".

1.The mathematical one :
It is an abstraction, a concept that dont need anything else than "the line".
(Sure you can construct the line with points, but also the point do not need a counterpart to exists, so it is conceptual)

2. The physical one :
I prefer to say, "the knowledge-linked one".
The line exists because there is something around the line, so here the plane.
You can consider the plane or the line to be also conceptual, but they can not exists without the existence of what they are not.
Line is not the plane.
The plane is not the line.
Line and plane together are "knowledge-linked", they can not exists "in term of knowledge" one without the other.
(The plane can also exists without the line too... but you have to propose somethig else to "contradict" the plane).

Whats fascinating here is, that because the line is infinitesimal thick, the line is completely determined by the plane. The line is what the plane is not.
It is a relational way to think of the existence of the object.

But like you probably know the 2 definition is not what mathemaicians do (they are (and this is how i understand the term) unintuitive).
Therefore i consider that there is at least two mean to do mathematic and other civilisations could do mathematic differently as we actually do.

I have spoken of the line but you can also speak of the numbers.
In a relational way to think mathematic, there it is nonsense to talk about 1 without opposing (contradict, link in a relational way) it with 0.
1 can not exists without 0.
0 can not exists without 1
1 and 0 are linked together in a relational way.

When you use those definitions and consider that 1 mean "all" and 0 "nothing", you understand easyly that 1 can not exists and 0 can not exists fully.
When you use the "degrees" from 0 to 1 you see that soon you reach 1, because 0 become smaller, 1 become less existant (because 1 depend on his counterpart 0 and this counterpart become less existant).
This way of thinking avoid the possibility of singularities like infinite and 0, and you have a circle (you go from almost 1 to almost 0) instead of a simple line.

[paul cotter]

??

[talanum1 (OP)]

Take a line on a piece of paper. Mathematics says a line is infinitessimaly thin. However our experience says a line has finite thickness otherwise it would be invisible. Also our physics says there is a molecule next to the line.

[paul cotter]

Mathematics MODELS the line as infinitely thin. A real world line will obviously not match this definition, so what? You could of course, specify a particular minimal width to your line.

[talanum1 (OP)]

But infinitely thin means invisible or worse: non-existing - unintuitive.

[Origin]

But infinitely thin means invisible or worse: non-existing - unintuitive.

Yes a line in mathematics has no width, that means it is an abstraction.  If abstract thinking is a problem for you then mathematics in general will be a problem for you.

[Deecart]

Yes a line in mathematics has no width, that means it is an abstraction.

Thats how actual mathematic work (and this has been already explained). 

If abstract thinking is a problem for you then mathematics in general will be a problem for you.

Why do you say that ?
The question is : "Is mathematic unintuitiv ?" (pretty simple question), not if "you" or someone else think it is good or bad, or even if it is the right way or the wrong way to do mathematic.

You dont know, personaly, if mathematic will or can evolve in some other direction.
Actualy, mathematic is unituitiv.

[Colin2B]

Actualy, mathematic is unituitiv.

Why do you say that?
I find it very intuitive

[Deecart]

Actualy, mathematic is unituitiv.

Why do you say that?
I find it very intuitive

Because i think intuition has something to do with reality.
Instead, mathematic is "a chimera" (build from various things that do not belong together in reality).

I have just read that :

Here's an old mathematical joke.
How do you get an elephant into a jam jar?
Consider an elephant outside a jam jar, then perform a trivial inversion of vector space.

https://www.thenakedscientists.com/forum/index.php?topic=80604.540

This should explain what i think about "the reality" of mathematic.

[paul cotter]

If the "reality" of mathematics was in doubt, we would still be living in mud huts.

[Deecart]

If the "reality" of mathematics was in doubt, we would still be living in mud huts.

No.
You are here talking of physic who rely on SOME usage of mathematic.

[Origin]

Why do you say that ?

Because I think it's an accurate statement.

The question is : "Is mathematic unintuitiv ?" (pretty simple question), not if "you" or someone else think it is good or bad, or even if it is the right way or the wrong way to do mathematic.

I didn't say anything about good, bad, right or wrong.
My point is if you have difficulty in thinking in the abstract then mathematics would be unintuitive.  If you disagree that's fine and we can discuss it, but there's no reason to discuss something I didn't even say.

[Kryptid]

Some aspects of mathematics are unintuitive. For a lot of human history, zero, negative numbers and imaginary numbers weren't even conceived of.

[Deecart]

Some aspects of mathematics are unintuitive. For a lot of human history, zero, negative numbers and imaginary numbers weren't even conceived of.

You mean 0 was not understand by babylonian scientists ?
No, they know about, but they had some intuitive comprehension of the "0".
And everytime 0 appeared, they discarded this "unusual" possibility.
They used more intuitive comprehension of mathematical objects.

I should say that it’s not quite true that the Babylonians didn’t have a symbol for zero. In Plimpton 322, the tablet we studied in class, there are some gaps between numerals that represent zeros in the middle of a number, the way the 0 in 101 represents zero tens. Later, they added a symbol for zero, but it was only used for zeroes that were in the middle of the number, never on either end. That way they could tell the number 3601, which would have been written 1,0,1, from 61, which would be written 1,1. But 60 and 1 would always be written identically. They never made the leap to using a zero symbol at the end of a number to eliminate the ambiguity completely. The oldest documented zero is surprisingly modern: it’s in a temple in India, and it dates from about 875 CE.

One of the strange consequences of the lack of zero comes up in reciprocals. We usually think of reciprocals as number pairs like 2 and 1/2 that multiply together to equal 1. But Babylonian reciprocal tables, which made calculations quicker, listed any two numbers that multiplied to a power of 60 as “reciprocals.” For example, 5 and 12 are “reciprocals” in this sense because they multiply to 60. Why would this definition of reciprocal make sense? Because when you’re writing in base 60 without a zero, 60 looks just like 1! So do 1/60, 3600, and any other power of 60. It would be like us thinking of 4 and 25 as reciprocals because they multiply to 100. It would make some sense only if we didn't have a zero, so 1 and 10 looked the same.

https://blogs.scientificamerican.com/roots-of-unity/ancient-babylonian-number-system-had-no-zero/

[Kryptid]

You mean 0 was not understand by babylonian scientists ?

Humanity greatly predates that.

[Colin2B]

Because i think intuition has something to do with reality.
Instead, mathematic is "a chimera" (build from various things that do not belong together in reality).

Intuitive has nothing to do with reality. Intuitive means not requiring proof and much of maths is intuitive. In the example given, the line, no proof is required as it is a defined concept which is obvious - if the line has thickness then it is a rectangle or rod.
Similarly, a+b=c is intuitive, indeed to try and prove it can be very difficult.

Maths is a language and can be used to describe real and imaginary, abstract and concrete, true and false, intuitive and unintuitive.
However, to describe all mathematics as unintuitive is to fall into the trap of confusing some and all. @talanum1 has already fallen into this trap with his false logic, not realising that a logically correct syllogism can give a false answer if one of the premises is false. You also fall into this trap here:

I have just read that :

Here's an old mathematical joke.
How do you get an elephant into a jam jar?
Consider an elephant outside a jam jar, then perform a trivial inversion of vector space.

This should explain what i think about "the reality" of mathematic.

What makes us laugh here is the intuitive understanding that the answer is wrong. This shouldn’t surprise us, used incorrectly any language will give wrong answers.

If the "reality" of mathematics was in doubt, we would still be living in mud huts.

No.
You are here talking of physic who rely on SOME usage of mathematic.

That is incorrect. Not only is @paul cotter is talking about reality in a much wider sense than you are, but the whole field of applied mathematics deals with reality (not the same as right and wrong answers). That field covers not only physics, but engineering, economics, biology, psychology, forecasting, modelling etc.

[Deecart]

Intuitive has nothing to do with reality. Intuitive means not requiring proof and much of maths is intuitive.

You are totaly wrong.
Intuitive is the adjective related to intuition.

Intuition is a faculty some sentient beings use to do some "calculation" without be able to express how they did the "calculation" (you could understand this if you would study the biological neuronal networks).
Intuition can be opposed to rationalisation.
When you use rational thinking you are able to follow (and express, so the use of a language) every step of the "calculation" and for that you use some logic :Basicaly the aristotelian logic.
But ... you have other logics and this is where the things can become tricky if you want to go further.

There Are Many Logics

When we examine the semantics of natural language we see enormous diversity in the kinds of expressions that we can generate. These are often a stimulus for new developments in logic, as researchers try to invent new formal languages (or modify old ones) that do a better job of capturing the semantics of particular aspects of natural language.

What you study in a first class in symbolic logic is actually a specific type of propositional logic — classical, truth-functional propositional logic.

Other logical systems have been developed that are “propositional” in that they deal with logical relations of propositions take as wholes, but they may not be “classical” or “truth-functional”.

In classical logic we assume that propositions can only be true or false, not both, and there are no third options available. Non-classical logics drop or modify one of these basic assumptions.

There are systems called “intuitionistic logics”, for example, that were designed to model the logic of “constructive provability”. We don’t need to go into the details of what that means, but it turns on the distinction between knowing that a statement is “true” and knowing that one can actually construct a proof — a derivation — of that statement.

In classical logic you can prove that certain statements are true, without actually having to construct a proof for them. We can do this, for example, by showing that the negation of a statement, not-P, leads to a contradiction, and from that fact jump to the conclusion that P must be true. In classical logic, any statement that entails a contradiction must be false, and by double negation we see that not-(not-P) = P, i.e. that P must be true.

For various reasons the founders of intuitionistic logic wanted to disallow proofs like this.

https://criticalthinkeracademy.com/courses/2514/lectures/751634


When you say "mathematic" is intuitiv or not you have to understand that you are not talking about mathematic at all (is a chair intuitiv ? is physic intuitiv ? is logic intuitiv ? is athetism intuitiv ?) but you are talking about the person who use mathematic.
You have missed this point, doing the confusion between the result of human action and the human action itself.

Now, do you really think mathematicien can say : Hey guys i have some intuition that this is right, but you need to believe me because i can not prove you this because of course mathematic is intuitiv ?
What a laugth !

No, mathematical activity is unitituitiv, every step need a proof (so only rational thinking) and when some very profound concept are not  YET proved by some other more profound concepts, we call it "postulate".
But "we" dont care (mathematicians) if the postulate is true or not...
Because... we dont deal with reality.
You can change your postulate and do whatever you want:  you do chimeras at will.
.

In the example given, the line, no proof is required as it is a defined concept which is obvious - if the line has thickness then it is a rectangle or rod.

What a laught.
You just proved that the line need to be infinitesimal because if it isnt it is the other form you have already imagined (the chimera).

Similarly, a+b=c is intuitive, indeed to try and prove it can be very difficult.

If it can be proved like you say (difficulty is not impossibility) it contradict your definition of intuition...
You are not consistent.