Do they really exist? I once saw a proof showing that they were the same as positive numbers.

 

I think it may have come from Dave. I will try to look for it.

 

If negative numbers are the same as positive, does that mean imaginary numbers are just a fabrication of man?

Of course they "exist". If you are in debt, you have a negative amount of money. Simple as that. And, as for imaginary numbers, if they don't "exist", I feel sorry for everyone who's been relying on QM this whole time, seeing as QM relies quite a bit on imaginary numbers.

[math]i=\sqrt{-1}[/math]

 

I was referring to a proof I saw that showed that they + and - numbers were the same

They exist as much as any number can be said to "exist," I imagine. I think it's misleading to speak of a number "existing" in reality. I take a positivist stance: negative numbers are helpful in describing things we observe and things we do. So are imaginary numbers, infinitessimals, and infinity. I've never seen an imaginary number or a negative one, but I've never seen a positive number, either.

I was referring to a proof I saw that showed that they + and - numbers were the same

That might have been a trick proof (i.e. one that's not really a proof, but a clever argument that looks like a proof), or else there is something about "being the same" that I'm not getting. A negative number will never equal a positive number. A negative number and a positive number can have the same absolute value, but beyond that I don't know what to make of the word "same."

Negative numbers and positive numbers are not the same. Think about it for a second. A positive plus a positive is always greater than or equal to zero, yet a positive plus a negative can take on the value of any positive or negative value. Therefore, + does not equal -.

I THINK it was in the "Ending the 0.999~ = 1 debates" thread.

You mean this "proof?"

 

-1 = -1

-1 / 1 = 1 / -1

sqrt(-1/1) = sqrt(1/-1)

sqrt(-1) / sqrt(1) = sqrt(1)/sqrt(-1)

i / 1 = 1 / i

i^2 = 1

-1 = 1

 

The fallacy is pretty obvious.

I think there has been a debate already on wether or not numbers exists. They are usefull to help us understand real-life stuff but they do not really exist in "reality".

In no way negative numbers are equal to positive ones but if you were to define negative numbers you would need only the existence of positive numbers in order to do so.

 

Mandrake

Of course they "exist". If you are in debt, you have a negative amount of money.

Debt is a tricksy fat example because the "amount of money" as an entity is still positive - it's only the person who owns it that has changed. The debt itself is negative, but it's an abstract concept so I'm not sure it answers the question.

 

Actually, iirc this has come up before.

All numbers exist as only abstract entities, maths is an abstarct subject which has no intent to describe 'physical reality' (if your interested in why maths does seem to be useful in describing physical relaity look up Wigner's essay on the subject).

"5" is abstract but "5 dollars" is not (insofar as your average indebted person is worried about degrees of abstraction).

Actually, iirc this has come up before.

 

I do believe the aforementioned thread lies in Applied Math somewhere.

i^4=1

How about when solving movement questions.

What's the acceleration of the car?

-3m/s,-5/s

It's -2m/s^2 or 2m/s^2 towards the negative direction.

So related to negative and positive questions?

How about when solving movement questions.

What's the acceleration of the car?

-3m/s' date='-5/s[/b']

It's -2m/s^2 or 2m/s^2 towards the negative direction.

So related to negative and positive questions?

 

I don't understand.

 

Negative/positive questions?

When a car accelerates towards the positive side with 3m/s^2.

We have many different ways to state it.

Therefore, I think positive number is equal to negative number if we change the "side".

i^4=1

 

What does that have to do with anything?

When a car accelerates towards the positive side with 3m/s^2.

We have many different ways to state it.

Therefore' date=' I think positive number is equal to negative number if we change the "side".[/quote']

 

No, because your car could still be moving forward yet have a negative acceleration.