Thread: Mathematical Numbers are Theoretical; Not Proven

Your wording is all very confusing to me. First of all, just because there are an infinite number of numbers between 0 and 1 doesn't mean you will never reach 1. There are an infinite number of numbers period. Every number exists. Saying you can't reach it because there are an infinite number of numbers in between just doesn't make sense. Also, you can add an infinite number of numbers and get a whole number.

The number 1 does exist. Its value is 1.0000000000000000000........ repeating forever. It is also equal to .999999... repeating forever. Source

Second, saying numbers are only theoretical doesn't make much sense. They aren't real, but that doesn't exactly make them theoretical. Within the realm of mathematics a number has a precise and defined value. It isn't theoretically 1, mathematically it is 1. The only reason you can't have 1.33333333333333333........ eggs is because the real world isnt infinitely divisible. In math, things are, so you could have that many eggs. Infinity doesn't exist in the real world, and I think that is what is confusing you.

I'm sorry if my response is vague or doesn't exactly address what you were saying. Your post kind of confused me and i couldn't tell exactly what you were trying to say.

I have no idea what the OP is trying to convey. Not only am I unable to decipher the relationships between the various points made, but I also cannot understand what most of the statements mean at all, even in isolation. It's almost as if the post is in another language. I'd be happy to reply, but I need a rephrase here.

If 1 is impossible to reach, then it is only theoretical, not proven.

The argument fails here, as 1 is not impossible to reach. Just because there are an infinite amount of numbers between 0 and 1, this does not stop you from reaching it.

In the same way that there are an infinite amount of ways you can orientate a shape. That doesn't stop you from rotating it 90 degrees.

Infinite gradient =/= infinite magnitude

What you're saying is the same as the movement paradox. It's a nice theory, but it doesn't work.

Originally Posted by '[SomeGuy

Example of Real Life Numbers: There are two eggs on a table. It's pretty obvious that there are two eggs: Therefore, Real-Life numbers are already proven to exist. But mathematical numbers are only theoretical. You can't have 1.333... eggs.

There is no such thing as "two eggs" in real life. That is just a mental model. No two eggs are identical. You just classify those two different objects into an artificial category.
Therefore eggs do not exist?

You're basically making no sense at all.

Please try and reiterate a little more succinctly.

I think it has been determined that this argument is full of holes. Big ones.

Ha, sorry if it sounds a bit confusing. I'll try writing it with more form and repost.

Math is the one science that is concrete and universal.

Gravity pulls mass together - theory
Genetic mutations and natural selection creates evolution - theory
God created everything - myth
1 * 10 = 10 - fact

Math is 100%, unlike every other science. It's not based on observable reality (which is variable), it's based on absolutes.

Originally Posted by ninja9578

Math is the one science that is concrete and universal.

Gravity pulls mass together - theory
Genetic mutations and natural selection creates evolution - theory
God created everything - myth
1 * 10 = 10 - fact

Math is 100%, unlike every other science. It's not based on observable reality (which is variable), it's based on absolutes.

Ninja, I agree with you. My partner in philosophical agreement!

I love maths, I just was having some confusion about why whole numbers are possible. I see what my holes are, so maybe we should forget this thread...lol. I kind of answered my own question earlier today. No need to rewrite it.

The problem is that the absolutes are completely arbitrary, so mathematics isn't an entity at all.

I could say that 3 * 4 = 2, and 2 * 9 = 8, and 6 * 6 = 6, and so on (and then 1 * 10 = 0). It wouldn't be wrong, in fact it would form a completely coherent system. The thing is that whether it has any relevance to what I'm doing depends solely on what I'm trying to do.

Maths generalises reality, that's all.

Maths is reality. Maths is the purest form of science and study you can find.

Originally Posted by Xei

The problem is that the absolutes are completely arbitrary, so mathematics isn't an entity at all.

I could say that 3 * 4 = 2, and 2 * 9 = 8, and 6 * 6 = 6, and so on (and then 1 * 10 = 0). It wouldn't be wrong, in fact it would form a completely coherent system.

It would be wrong, unless you changed the meanings of the symbols. Humans invent the symbols, but not the realities they represent.

Maths is reality. Maths is the purest form of science and study you can find.

Actually, there will always be statements that you can't prove with any set of mathematical rules.

Thus, truth is higher than mathematical proof.

Read about Godel.

It would be wrong, unless you changed the meanings of the symbols. Humans invent the symbols, but not the realities they represent.

You can change the symbols to mean anything you want, and the rules of manipulating the symbols. Each time you would get a new, different system, only true in itself. You say one system of maths is real; then what about other, contradictory systems?

If you make + = subtraction, then 2 + 2 = 0, where the standard system is 2+2=4. There are an infinite amount of systems you can make, is what he's saying.

Numbers are the ghosts and spirits of the rational world.

Think about this: you have some mathematical system, S, which you claim can prove whether any statement is true or not.

If this is so, it should be able to determine the truth of the following statment, G:

G: G cannot be proved by S.

If S says yes, I can prove G is true, then it has contradicted itself, and so S is actually fundamentally wrong.

The other option is that S cannot determine whether or not G is true, in which case it is limited in its 'monopoly' on truth. However, we can clearly see that G is true.

Therefore, there is no system of mathematics which can determine everything which is true.

Originally Posted by grasshoppa

Numbers are the ghosts and spirits of the rational world.

I did your mom.

Originally Posted by [SomeGuy]

I did your mom.

Perhaps, perhaps not.

Originally Posted by grasshoppa

Perhaps, perhaps not.

No, I'm sure I did.


Anyway, Maths:
2+2=4, correct? We all agree.


Moderators, please delete this topic, it was just a test.

Originally Posted by grasshoppa

Numbers are the ghosts and spirits of the rational world.

lol, this bullshit in the middle of actual discussion. I agree with Universal. The way we communicate math is made by mankind, but the truths represented are universal constants.

Originally Posted by Xei

The problem is that the absolutes are completely arbitrary, so mathematics isn't an entity at all.

I could say that 3 * 4 = 2, and 2 * 9 = 8, and 6 * 6 = 6, and so on (and then 1 * 10 = 0). It wouldn't be wrong, in fact it would form a completely coherent system. The thing is that whether it has any relevance to what I'm doing depends solely on what I'm trying to do.

Maths generalises reality, that's all.

Originally Posted by Xei

You can change the symbols to mean anything you want, and the rules of manipulating the symbols. Each time you would get a new, different system, only true in itself. You say one system of maths is real; then what about other, contradictory systems?

I think you are misunderstanding the difference between the language of mathematics and the world of mathematics. It is similar to the observable universe and human language. There is (so far) only one observable universe. It exists without language. As humans, we create language to describe it. So far, we have created hundreds of coherent sets of languages (english, japanese, hungarian, etc...) that all make sense describing the world around us. Even though they use completely different sets of rules and sometimes symbols, they all describe one unchanging world. Calling a dog different words doesn't change the fact that its a dog.

The world of math is exactly the same. There is only one world of mathematics, and it exists without language. You can use different languages to describe it (decimal, hex, binary, etc...) but they only make sense if they are coherent throughout the whole world of mathematics. You say you can throw random symbols together and they would make a coherent system...it doesn't work like that. I can say "asjdh jkahsldkah jvhkjlhl" and tell you it makes sense in another language, but it doesn't mean it does. Just like you can spout gibberish in language, you can spout gibberish in math. Just like a dog is a dog no matter what the name, adding the idea of one to the idea of one will create the idea of two. Changing the symbols used to represent that just changes how it looks on paper.