Maths, 0, and The Mysteries of the Universe

[Ironsights]

given mus's math history, he might not have known what you meant...

 

sorry mate. its a cheap shot, but I couldnt resist.

[Eliwan]

Actually Mus hasn't made mathematical errors, just never knowing if stuff is times 1+(1-x), divide by 1-x, or additive.

 

Also, yes. Yes it is.

[Mus]

given mus's math history, he might not have known what you meant...

 

sorry mate. its a cheap shot, but I couldnt resist.

 

My maths history is perfect. I have never made any mathematical errors, I only slip up on the game mechanics. Those are two different things. I knew exactly what Eliwan meant, I only corrected him from a maths point of view because I didn't like the implication that 0 isn't a number. It's just a pedantic mathematician thing.

[Ironsights]

but 0 technically is NOT a number, it is the absence of all numbers ;)

 

to quote einstein 'if you can't divide by it, its not a number'

[Mus]

but 0 technically is NOT a number, it is the absence of all numbers ;)

 

to quote einstein 'if you can't divide by it, its not a number'

 

I'm sorry but you are totally wrong here. Also, Einstein was a physicist not a mathematician. The definition of a number isn't 'can I divide by it'.

 

In number theory it is well known that zero is a number. It is an element of the set of Complex numbers, Real numbers, Rational numbers, the Integers and also even the Natural numbers if you decide to include zero as a Natural number. However, most of the mathematicians at my university don't include zero in the natural numbers.

 

Zero is not the absence of all numbers, it is a number in its own right. The absence of all numbers is the empty set.

[Ironsights]

;)

[Nuparu]

I'm sorry but you are totally wrong here. Also, Einstein was a physicist not a mathematician. The definition of a number isn't 'can I divide by it'.

 

In number theory it is well known that zero is a number. It is an element of the set of Complex numbers, Real numbers, Rational numbers, the Integers and also even the Natural numbers if you decide to include zero as a Natural number. However, most of the mathematicians at my university don't include zero in the natural numbers.

 

Zero is not the absence of all numbers, it is a number in its own right. The absence of all numbers is the empty set.

 

Zero is a Complex/Real/Integer... but it's kind of a different number.

 

It has special exceptions in it's own right (You can't divide by it, you can't negate it because there's nothing to negate).

 

I never considered it an actual number, just a digit/an absence of a number. But, it all depends on how you view it.

[Mus]

Zero is a Complex/Real/Integer... but it's kind of a different number.

 

It has special exceptions in it's own right (You can't divide by it, you can't negate it because there's nothing to negate).

 

I never considered it an actual number, just a digit/an absence of a number. But, it all depends on how you view it.

 

Fact is, zero is a number. You cannot argue with that. Your arguments for not considering zero as a number are very weak, and it doesn't depend on 'how you view it'. There is no point in trying to argue with something that has already been solidly defined/proved in maths because you will always lose.

 

I will give you one (of many) examples which shows how maths wouldn't work if zero wasn't a number:

 

The set of integers together with the binary operation + (addition) forms a group, (Z,+). Now, by definition of group, it must contain an identity element for the binary operation, in this case for addition. Zero is the identity for addition, so if you do not consider zero to be a number, then zero is not in Z, so (Z,+) wouldn't be a group and the whole of Algebra would collapse, which would lead to Quantum Mechanics to collapse as well as many other areas of both Maths and Physics.

[RedHydra]

I've always thought that zero is considered a 'real' number, so long you can use operations with it and find accurate results.

 

Mmm...this is an interesting off-topic discussion.

 

Regarding AoS updates, we're probably going to delay it for about a month for those who haven't bought HotS. However, we'll still conduct beta tests for new heroes. So we're going to need participants with HotS access to help out.

[Ironsights]

If zero is "real" then why is it that my hand is empty when I am holding zero dollars?

 

If my ledger says I have money, its a positive number. If I owe money, its a negative number. If I lack any form of money, its zero. Zero is thus the absence of money, and is neither positive nor negative. The only time, other than Zero, a number is neither positve nor negative is the 'imaginary' number (i) used to root negatives.

 

By this thought process, and using math terms, zero must then be imaginary.

 

If my imaginary friend is not real, neither is zero.

[shogigut]

If zero is "real" then why is it that my hand is empty when I am holding zero dollars?

 

If my ledger says I have money, its a positive number. If I owe money, its a negative number. If I lack any form of money, its zero. Zero is thus the absence of money, and is neither positive nor negative. The only time, other than Zero, a number is neither positve nor negative is the 'imaginary' number (i) used to root negatives.

 

By this thought process, and using math terms, zero must then be imaginary.

 

If my imaginary friend is not real, neither is zero.

 

Excuse me, "real number" is a mathematics term

[Mus]

If zero is "real" then why is it that my hand is empty when I am holding zero dollars?

 

If my ledger says I have money, its a positive number. If I owe money, its a negative number. If I lack any form of money, its zero. Zero is thus the absence of money, and is neither positive nor negative. The only time, other than Zero, a number is neither positve nor negative is the 'imaginary' number (i) used to root negatives.

 

By this thought process, and using math terms, zero must then be imaginary.

 

If my imaginary friend is not real, neither is zero.

 

You are correct in saying that zero is neither positive nor negative, but that's it. You also said zero is real but you clearly have no idea what that means. A number is real if and only if it is in the set of real numbers, R, which contains all rational and all irrational numbers.

 

You also don't seem to know much about imaginary numbers, seeing as you compare them to imaginary friends, suggesting they do not exist. An imaginary number is defined to have the form b*i where b is real. Since zero is a real number, you can say that 0*i is imaginary. But 0*i=0. So zero is both real and imaginary. Imaginary numbers come up all the time in physics and engineering, not just in abstract maths.

 

If you sketch out the complex plane (real numbers on the x axis and imaginary numbers on the y axis) and you exclude the origin because you think zero is not a number, then how would you calculate contour integrals? Without the origin, you have a hole and so Cauchy's theorem no longer applies.

[Ironsights]

I very much understand real numbers in mathematics. I put real in quotes because I was implying real as in actually exists not as in a Real (math term) number.

 

Also, imaginary numbers are in the form b*i where b is real...thus b is real and i is imaginary, that doesn't mean i exists...its still imaginary. These are filler numbers, place holders designed to allow complex formulas to be completed without the need for actually defining what cannot truly exist.

 

As for you cauch, just 'cause it has a hole in it doesn't mean it isn't any good any more. hell, my cauch has lots of holes, its pretty old...

 

Also, you continue to use physical definitions to explain a metaphysical concept. You cannot define 0 as anything, it is a lack of things. You cannot hand me 0. You cannot show me 0. What exactly is 0 then? It is forced to be a concept, and while a concept can be used, it cannot be possessed. If it cannot be possed, it is not physically real. If not physically real, it is therefore imaginary.

 

----

Speaking only of mathematics, 0 is also quite hard to define. It is neither positive nor negative. It consumes any number multiplied by it, refuses to alter a number in any fashion when added or subtracted, and simply cannot be used in division. The only 'use' 0 has other than being the lack of other numbers is as an arbitrary center point for graphing...but even there it is without direction, it is the center. As such, it is once again without definition, thus not truly existing.

 

Isn't philosophy fun?

[Mus]

I very much understand real numbers in mathematics. I put real in quotes because I was implying real as in actually exists not as in a Real (math term) number.

 

Also, imaginary numbers are in the form b*i where b is real...thus b is real and i is imaginary, that doesn't mean i exists...its still imaginary. These are filler numbers, place holders designed to allow complex formulas to be completed without the need for actually defining what cannot truly exist.

 

As for you cauch, just 'cause it has a hole in it doesn't mean it isn't any good any more. hell, my cauch has lots of holes, its pretty old...

 

Also, you continue to use physical definitions to explain a metaphysical concept. You cannot define 0 as anything, it is a lack of things. You cannot hand me 0. You cannot show me 0. What exactly is 0 then? It is forced to be a concept, and while a concept can be used, it cannot be possessed. If it cannot be possed, it is not physically real. If not physically real, it is therefore imaginary.

 

----

Speaking only of mathematics, 0 is also quite hard to define. It is neither positive nor negative. It consumes any number multiplied by it, refuses to alter a number in any fashion when added or subtracted, and simply cannot be used in division. The only 'use' 0 has other than being the lack of other numbers is as an arbitrary center point for graphing...but even there it is without direction, it is the center. As such, it is once again without definition, thus not truly existing.

 

Isn't philosophy fun?

 

You argue more with philosophy rather than maths, and philosophy is a load of rubbish. Zero is very well defined in maths, it exists in maths, Just because you cannot see it in real life doesn't mean it cannot exist. I have already shown how Algebra wouldn't be possible if zero wasn't a number.

 

As for your silly argument about imaginary numbers not existing in real life, well they do. In physics we use them all the time. One example is for AC circuits. The current flow and the voltage are given in complex form, they contain 'i' in them. We also use imaginary numbers to make working with cosines and sines easier:

 

cos(x) = (1/2)*[exp(ix)+exp(-ix)]

sin(x) = (1/2i)*[exp(ix)-exp(-ix)]

 

@Midknight: There isn't really anything to discuss per say, these guys just fail to understand something that is well known. It's futile to try to argue against something that has already been absolutely proven in maths.

 

And philosophy is the kind of rubbish where people say that 0.9 recurring does not equal 1, even though there is a mathematical proof to show that it does. Another example of how philosophers waste their time.

[Wrath]

As for your silly argument about imaginary numbers not existing in real life, well they do. In physics we use them all the time. One example is for AC circuits. The current flow and the voltage are given in complex form, they contain 'i' in them. We also use imaginary numbers to make working with cosines and sines easier:

 

cos(x) = (1/2)*[exp(ix)+exp(-ix)]

sin(x) = (1/2i)*[exp(ix)-exp(-ix)]

 

You did not just make working with sin and cosine look easier. In any case, refer to Midknight's ninja post. :P

[Mus]

You did not just make working with sin and cosine look easier. In any case, refer to Midknight's ninja post. :P

 

It may not look easier at first, but it actually does make everything go a lot smoother and quicker. A lot of work is saved by converting to exponential form when trying to integrate in physics. No one uses sines and cosines.

[Nuparu]

It may not look easier at first, but it actually does make everything go a lot smoother and quicker. A lot of work is saved by converting to exponential form when trying to integrate in physics. No one uses sines and cosines.

What does exp() mean?

 

:S

[BestPlayer]

It means eksponential, something you learn in skool, using an eksponential funktion to kalkulate things like interest rate.

 

Anyway Mus, I don't know why you need to stuff it down eweryones throat that you're good at math. Hey, I'm more than happy that I don't deal in mathematiks daily, and I hawen't sinse I was out of highskool. You are most sertainly better at mathematiks than me, but why do you need to konsistently kreate arguments about it? Someone misunderstands a konsept, and it kauses you to go out on some huge tangent, in the end shallenging their intelligense and general aptitude. I don't know why you do this kind of thing, you're a better person than that :)

[BestZeratul]

Agree with soed, having studied math myself, I will add that everything you talked about is high school level maths, so for people who actually studied maths it only makes you sound pedant instead of knowledgeable.

[BestZeratul]

Btw Ironsight your arguments are flobing terrible, holy shap it's so flobing dumb to argue that 0 isn't a number because you can't hand 0, and then talk about imaginary numbers when i would have been a much better choice for your argument in the first place.

 

Anyway instead of trying to sound knowledgeable Mus should just have explained how integers are defined, I'm too lazy to list all the axioms and I studied maths in French so I don't want to do it but feel free to google it.

 

TLDR : 0 is a number

[BestPlayer]

I think this klip is symptomatik of the diwide between ironsights and Mus. They are perhaps rather alike, yet still different, and may at times feel out of synk with eashother.

At the end of the day we are all human, we all make mistakes, but we should be alright in time. Like one big happy family, all orignating from Afrikan. We all hawe blak souls.

[Mus]

My intention wasn't to belittle anybody. I thought that giving some examples to demonstrate how zero needs to be a number I would get my point across better. I admit I did become frustrated with the arguments that Ironsights was using. Chob is right in saying I could have just stated some axioms but those are kind of dull in my opinion, I like giving examples because they are interesting.

 

Edit: Soed as for going off at a tangent, I was only trying to respond to Ironsights points. He said that imaginary numbers are fillers for things that cannot truly exist. That's how I ended up talking about physics lol.

[BestZeratul]

People in general are making the mistake of using words like "true" in math anyway. The only thing you measure in math is coherence with your axioms in the first place, because you are always working with a system of axioms that is completely arbitrary (granted when it comes to integers it's stuff you use in real life but my point still stands).

 

What it means is that arguing about stuff like 0 being a number is arguing about a convention mathematicians use for convenience and is thus retarded and pointless, because there is no reasoning behind it besides convenience.

[BestPlayer]

So what you're saying is that 0 isn't a number? Lol it was always obwious like when I hold 0 pankakes in my hand, I don't got any pankakes? Lmao why ewen argue when its so obwious????? :)))

 

@Mus

I understand, and you like what you do (I'm assuming you're studying some sort of mathematikal subjekt, giwen your insistanse on always arguing and offering your pow in sush talks. It would just seem pertinent and fitting, forgiwe me if I am wrong.

 

But you just need to realise people here straight up might not know what you're talking about. Aktually that seems rather ewident. Then your rather aggresiwe behawiour komes off as krass to people who do understand, and probably arrogant to those who don't. There is no need for it :)

[NoWaterJustIce]

So what you're saying is that 0 isn't a number? Lol it was always obwious like when I hold 0 pankakes in my hand, I don't got any pankakes? Lmao why ewen argue when its so obwious????? :)))

 

I had 2 pancakes for breakfast this morning and they were yummy :)