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**xCEssIve_MAthS****Member**- Registered: 2005-04-11
- Posts: 7

All numbers are created by one person. Therefore all equations are only a figment of this person's imagination. Think about it.

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**I love pi****Member**- Registered: 2005-06-30
- Posts: 11

please continue.........................

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Maybe...but that one person made all those rules. He had two objects, each meaning 1 (1 stick and 1 stick). He thought "ah, perhaps there is a way to combine both the 1s?". And he probably named that number 2. And then with the 3 1s, and so forth until he became so confused he didn't want to continue.

All this information from this person was expanded, and other people made their own stuff up, with their own rules. All the stuff was passed on, and that is probably how we came up with all these formulas today.

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

It's pretty amazing how all of it builds up. Maths is a lot about understanding one concept, using that to build another, then using that to build another and another etc.

If you were to explain a really hard concept to someone who didn't know anything about maths you would have to trace your explanation all the way back to the basics.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

What I have recently found increasing interesting is that you can prove that numbers exist. Once one accepts ZF set theory, and then defines the natural numbers, you can prove that the natural numbers do in fact exist. Then once you define addition, you can prove that addition exists. You can do exactly the same with multiplication and exponents. And then the same with the integers, rationals, and reals.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

All sounds like fun!!

But who makes the rules! i.e is a Glass half empty? or half Full?

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Anthony.R.Brown wrote:

But who makes the rules! i.e is a Glass half empty? or half Full?

Neither, it has 50% water(with it's impurities) and 50% air(with it's impurities).. No need to be negative or positive about what a glass contains, it just does

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Patrick

Quote:

"Neither, it has 50% water(with it's impurities) and 50% air(with it's impurities).. No need to be negative or positive about what a glass contains, it just does "

A.R.B

But I'm sure you are missing the % that is taken up by the internal lining of the Glass!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

The only thing that we can really conclude is that the glass is twice as big as it needs to be.

Why did the vector cross the road?

It wanted to be normal.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Another important point is!

Is it possible to fill a Glass with water 100% I think not! because water droplets are larger than air pockets,that Glass contains! so the answer must always be Only 99.99999....% possible!

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Is it possible to fill a Glass with water 100% I think not! because water droplets are larger than air pockets,that Glass contains! so the answer must always be Only 99.99999....% possible!

And how is it that you reach that conclusion? I don't agree with the first statement, but assuming it's true all you can say is that the glass contains less than 100%.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Ricky!

Quote:

"And how is it that you reach that conclusion? I don't agree with the first statement, but assuming it's true all you can say is that the glass contains less than 100%."

There are a lot of things you dont agree with! it would help your case,if you would first put forward you (FLT) Bet to me!! regardless of your source!

p.s as for your Quite above! "FILL A GLASS" is about trying to place 100% water within a "GLASS" not "GLASS ITSELF!" it just happens that because water cannot "FILL" everying hole within "GLASS" then its impossible to "FILL A GLASS" 100%..............

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

Anthony.R.Brown wrote:

Another important point is!

Is it possible to fill a Glass with water 100% I think not! because water droplets are larger than air pockets,that Glass contains! so the answer must always be Only 99.99999....% possible!

But everyone knows 99.99999...% = 100%

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Anthony.R.Brown wrote:

To Patrick

Quote:

"Neither, it has 50% water(with it's impurities) and 50% air(with it's impurities).. No need to be negative or positive about what a glass contains, it just does "A.R.B

But I'm sure you are missing the % that is taken up by the internal lining of the Glass!

What are you talking about? Filling a glass, means replacing air, in the space with the glass as it's boundaries, with water. So of course you could.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Ricky wrote:

What I have recently found increasing interesting is that you can prove that numbers exist. Once one accepts ZF set theory, and then defines the natural numbers, you can prove that the natural numbers do in fact exist. Then once you define addition, you can prove that addition exists. You can do exactly the same with multiplication and exponents. And then the same with the integers, rationals, and reals.

That could be circular logic, Ricky. For example, the premise is the set exists, after some certain deduction the number exists. The logic in the middle may be sound, but you should accept the premise first.

*Last edited by George,Y (2007-01-26 17:20:52)*

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

pi man wrote:

Anthony.R.Brown wrote:Another important point is!

But everyone knows 99.99999...% = 100%

Not me.

So far as I know, there is not a single material that is 99.999...% pure:

24K gold is 99.999999% pure,

Diamond can be even purer, but not with infinite 9's.

And that is how my chemistry teacher told me:" strictly there is no material pure up to now".

**X'(y-Xβ)=0**

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

I agree with you George. I was actually just trying to get Mr Brown riled up with the whole .9999... = 1 fiasco! For those who don't know what I'm talking about, see the threads dealing with .9 in the "This is Cool" forum.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

George,Y wrote:

pi man wrote:Anthony.R.Brown wrote:Another important point is!

But everyone knows 99.99999...% = 100%

Not me.

So far as I know, there is not a single material that is 99.999...% pure:

24K gold is 99.999999% pure,

Diamond can be even purer, but not with infinite 9's.And that is how my chemistry teacher told me:" strictly there is no material pure up to now".

You're mixing math and physics/chemestry in a way which isn't defendable - please don't. Mathematics is, deliberately, a system which isn't based on the 'world'. The ancient Greeks invented the system with axioms, proofs, etc, because of the view on the world they had - greatly influenced by thinkers like Plato. Physics and chemistry are greatly dependable on math, but they're based on observations of the 'world'. Since math is not based on how the 'world' works, you can't prove something wrong in mathematics by using science.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

George,Y wrote:

Ricky wrote:That could be circular logic, Ricky. For example, the premise is the set exists, after some certain deduction the number exists. The logic in the middle may be sound, but you should accept the premise first.

Not at all. That's exactly what an axiom is, George. Something taken to be true without proof.

If you have no axioms, then you can't do anything.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Ricky wrote:

George,Y wrote:Ricky wrote:That could be circular logic, Ricky. For example, the premise is the set exists, after some certain deduction the number exists. The logic in the middle may be sound, but you should accept the premise first.

Not at all. That's exactly what an axiom is, George. Something taken to be true without proof.

If you have no axioms, then you can't do anything.

And this is why I like mathematics so much. It's a system, nothing more, nothing less. A system, albeit very advanced, based on some basic ideas - which we prefer to call axioms. If you met a person with no knowledge of mathematics at all, you could explain even the most complex things - by traceing them all the way back to the axioms of mathematics.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Not at all. That's exactly what an axiom is, George. Something taken to be true without proof.

If you have no axioms, then you can't do anything.

-That is very interesting, Ricky. Can I call maths is based upon several beliefs???

-What if I have a different belief-I don't shrine the maths religion?

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Patrick wrote:

You're mixing math and physics/chemestry in a way which isn't defendable - please don't. Mathematics is, deliberately, a system which isn't based on the 'world'. The ancient Greeks invented the system with axioms, proofs, etc, because of the view on the world they had - greatly influenced by thinkers like Plato. Physics and chemistry are greatly dependable on math, but they're based on observations of the 'world'. Since math is not based on how the 'world' works, you can't prove something wrong in mathematics by using science.

On geology:

Geology is originated from the measuring trick of Egyptian officials-They need to remeasure and determin the segment line of farms after annual flood of the River Niles.

Ancient Greeks took over this trick and made further development, they derived premises and conclusions. But the premises were sure to be the right reflection of the nature at that time. Lines, triangles, and circles, to name a few. It was not until Euclid that all premises of geology was reduced to 4 axioms, leaving the other premises natural deductions of these four.

However, these four premises are intuitional, along with other hidden premises called defination.

At that time, due to lack of knowledge about the nature, the Ancient Greeks believed their premises are true reflection of the Nature, and they thus held it.

Several ancient Greek Philosophers (Including Zeno and Aristotle), did, seriously debated over the issue involving the defination of line, infinity, or other premises of geology.

Aristotle use several real world examples such as annual Olympic games, space, and "infinitely" divisible gold to support his "potential infinity" belief. He obviously assumed geology should be in accordance to the nature.

And in general, Ancient Greeks didn't give geology the privilage to enjoy some premises unnatural or irrational. In their view of academy, philosophy governs any other academics, and is the ultimate and correct understanding of the universe. This view is clearly illustrated by Aristotle's organization of his works.

Ancient Greeks, did, make a false assumption in another academy. They used to believe the thought was from the heart, but they altered to that from the brain after they gained enough knowledge of the human body.

I, therefore, have strong confidence in the Ancient Greeks in changing their premises in geology if they had got the chances to examine whether those premises are correct in nature.

Strangely enough though, I don't know from when the premises of maths has become irrefutable, unchangable of the maths system. Can I call the maths, the most logical and most rational major so far we human have, has an irrational and religious starting-point?

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

By the way, Logic has changed one premise in recent years, that is the choice of using " the existential assumption". Logic does look abstract and unscientific as maths. It can change its premise when people have got better study of reality, however.

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

I'm glad you agree with me, pi man.

**X'(y-Xβ)=0**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

That is very interesting, Ricky. Can I call maths is based upon several beliefs???

Yes, math is based upon a belief, or rather a series of beliefs. George, we have no other option, I certainly wish we did. If we start with nothing, then we can't do anything. Prove that an even plus an even number is even without using anything which comes from a belief.

What if I have a different belief-I don't shrine the maths religion?

That's the most wonderful thing about math! You *can* have entirely different beliefs. And if these beliefs turn out to work in solving problems which other mathematicians (or just people in general) are interested in, whether they be real or theoretical, you're beliefs will be accepted into math. If your beliefs yield no useful results, they probably won't.

Strangely enough though, I don't know from when the premises of maths has become irrefutable, unchangable of the maths system.

It isn't unchangeable, George. You can change it very easily. Simply come up with a new system which yields positive results, as math has done over the centuries.

Good luck!

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