I hate Maths and Physics...

[grey wanderer]

Maze1125

I still hold it's possible to divide by zero.
It's just that most of the time it comes up with answers most people don't like.

It can be made consistent, but not under the usual axioms of arithmetic or algebra. The funny thing is, the debate about division by 0 didn't really heat-up until 1734 when George Berkeley brought it up in a book whose content was levelled against Newton's form of calculus. There were a variety of problems with the math of the time and there were several mathematicains who would disagree and argue over the value (or legitimacy) of certain infinite sums. it took well over 100 years of effort before a solid foundation could be put underneath the ideas of derivatives, infinite sums, and irrational numbers. Thus was born the "limit" and several other interesting notions. That need-- the need to make every thing consistent and derivable from a few core ideas-- is (I believe) from whence the division legaleese arose. So you can see it's a tricky deal. Look into "The extended reals"(aka the affinely extended reals) or the "projectively extended reals" if you'd like to see two mathematical system where division by 0 is (under the appropriate conditions) allowed-- perhaps one of these two systems is more in keeping with your intuition...

[Edhellos]

phasmaexmachina

edhellos

Partial differentiation and multiple integrals was Calculus 3.

All I remember of my Calc 3 is the evil, evil trig identities.

edhellos

The parametric curves, vector calculus (grad, div, endless list of theorems) and Fourier Transforms/Series was Calculus 4.

I didn't do Fourier and Laplace stuff until I took Modeling Linear Systems. And that would be after a course on Differential Equation.

Oh, the differential equations course you took aside from all the calculus (I took it at the same time as Calculus 3), but you had a baby introduction to DEs in Calc 2.

Then after that, there's a second DE course...
And then, there's the PDEs course which was absolute death for me xd

[Awsumdude]

grey wanderer

Maze1125

I still hold it's possible to divide by zero.
It's just that most of the time it comes up with answers most people don't like.

It can be made consistent, but not under the usual axioms of arithmetic or algebra. The funny thing is, the debate about division by 0 didn't really heat-up until 1734 when George Berkeley brought it up in a book whose content was levelled against Newton's form of calculus. There were a variety of problems with the math of the time and there were several mathematicains who would disagree and argue over the value (or legitimacy) of certain infinite sums. it took well over 100 years of effort before a solid foundation could be put underneath the ideas of derivatives, infinite sums, and irrational numbers. Thus was born the "limit" and several other interesting notions. That need-- the need to make every thing consistent and derivable from a few core ideas-- is (I believe) from whence the division legaleese arose. So you can see it's a tricky deal. Look into "The extended reals"(aka the affinely extended reals) or the "projectively extended reals" if you'd like to see two mathematical system where division by 0 is (under the appropriate conditions) allowed-- perhaps one of these two systems is more in keeping with your intuition...

I suppose one thing to keep in mind after reading through those articles is that is possible in some special case to divide by zero and get infinite but for most intents and purposes infinite is considered undefined. However 0/0 is still undefined in any case as far as I can tell.

[A Lost Iguana]

Awsumdude

[...] However 0/0 is still undefined in any case as far as I can tell.

That can be defined, but it is indeterminate in value... >_>

[Awsumdude]

A Lost Iguana

Awsumdude

[...] However 0/0 is still undefined in any case as far as I can tell.

That can be defined, but it is indeterminate in value... >_>

Isn't that what is meant by undefined? Please explain.

[A Lost Iguana]

1/0 cannot be defined, to wit, there is no number a which satisfies the conditon '0 * a = 1'. However, this is not the case for '0 * a = 0', any number will do in that case. 0/0 is indeterminate.

[Maze1125]

A Lost Iguana

1/0 cannot be defined, to wit, there is no number a which satisfies the conditon '0 * a = 1'. However, this is not the case for '0 * a = 0', any number will do in that case. 0/0 is indeterminate.

In fact for 0x=1 can work if x is infinity.

[grey wanderer]

A Lost Iguana

1/0 cannot be defined, to wit, there is no number a which satisfies the conditon '0 * a = 1'. However, this is not the case for '0 * a = 0', any number will do in that case. 0/0 is indeterminate.

In one sense you are correct.. however, in another you are incorrect. In the affinely extended reals, 1/0 is defined to be infinity. Bear in mind that in this "unusual" context we have to give up several desirable properties... in particular, the affinely extended reals are no longer a ring. *Your* statement is still true; however in our new context, division is a strictly formal operation, and multiplication (by a nonzero element) is no longer reversible. C'est la vie... or in this case C'esl la math (or whatever the appopriate French word for math happens to be). It's all mentioned in the links that I provided.

[Lord Snoosh]

Blarf!

[A Lost Iguana]

grey wanderer

In one sense you are correct.. however, in another you are incorrect. In the affinely extended reals, 1/0 is defined to be infinity. Bear in mind that in this "unusual" context we have to give up several desirable properties... in particular, the affinely extended reals are no longer a ring. *Your* statement is still true; however in our new context, division is a strictly formal operation, and multiplication (by a nonzero element) is no longer reversible. C'est la vie... or in this case C'esl la math (or whatever the appopriate French word for math happens to be). It's all mentioned in the links that I provided.

Haha, I was not being absolute, but it is the simplest way I know to explain the difference between undefined and indeterminate.

[level9000]

I learned to like math a lot more thanks to khan academy, free site with physics and math tutorials all the way up to multivariable calculus.

[Suicidesoldier#1]

Maze1125

A Lost Iguana

1/0 cannot be defined, to wit, there is no number a which satisfies the conditon '0 * a = 1'. However, this is not the case for '0 * a = 0', any number will do in that case. 0/0 is indeterminate.

In fact for 0x=1 can work if x is infinity.

Well this thread was already necroed so...

No, zero is basically infinity nothing, ergo 0 an infinite amount of times will always be zero.

So zero x infinity = 0.


It is a legitimate lack of everything.

.000000000000000000001 x infinity could be infinity, but when you legitimately have nothing there is nothing.

In a way, 0 can be seen as the inverse of infinity, as everything is reduced to 0.

[Pseudo-Onkelos]

I like them, but I'm not good at either. That's why I'm trying to learn both . . . on my own.

[Ask Jappleack]

GOOd FOR YOU. Turn your frown upside down and worry about nothing, go and do as you please, though you did, so my post is redundant, except perhaps itd make you think twice about making a redundant thread.

[Ask Jappleack]

Suicidesoldier#1

Maze1125

A Lost Iguana

1/0 cannot be defined, to wit, there is no number a which satisfies the conditon '0 * a = 1'. However, this is not the case for '0 * a = 0', any number will do in that case. 0/0 is indeterminate.

In fact for 0x=1 can work if x is infinity.

Well this thread was already necroed so...

No, zero is basically infinity nothing, ergo 0 an infinite amount of times will always be zero.

So zero x infinity = 0.


It is a legitimate lack of everything.

.000000000000000000001 x infinity could be infinity, but when you legitimately have nothing there is nothing.

In a way, 0 can be seen as the inverse of infinity, as everything is reduced to 0.

i have a unniverse full of empty boxes.
They are all empty, how much boxes contain anything? theres infinite boxes.

I'll give you a hint.