mathematical theory

FrostedNipple

FrostedNipple

FrostedNipple

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right, im having an argument with a m8, i am saying that if you divide a number by 0 then you get infinity, he is saying you cant divide by 0, and backing up his ideas with a pizza theory (ie he cuts it up)

im basing my knowledge on my physics teacher, i think i heard him say something about it!

who is right?

FN
 
It doesn't matter, because the number "infinity" doesn't exist.

So the answer is useless either way.

Really though, he's right. If you divide something by 0 you might as well be doing nothing to it at all.
 
Jokester said:
As far as I'm aware infinity is defined mathematically as any real number divided by zero.

Jokester
Click to expand...

thanks

i wasnt saying that infinity had a value, he was just saying its impossible and has no meaning or name!, i was saying it was infinity :)
 
Jokester said:
As far as I'm aware infinity is defined mathematically as any real number divided by zero.

Jokester
Click to expand...

Isn't it more of a case of (lim x->0) k/x, where k is a real number? Rather than a straight k/0.
 
I thought that generally speaking, the answer is undefined when you divide a number by zero. Which basically means you can't do it.

There are some cases where dividing by zero is defined. For example the function (Sin x)/x is defined as 1 when x is 0.
 
Dave said:
Isn't it more of a case of (lim x->0) k/x, where k is a real number? Rather than a straight k/0.
Click to expand...

That's for tending to infinity I think, reaching infinity once the limit is reached at 0.

Could be wrong haven't done pure maths since uni.

Jokester
 
Psyk said:
(Sin x)/x is defined as 1 when x is 0.
Click to expand...

not on my calculator it isnt
hehe

Division is 'repeated' subtraction. Basics would convince you logically.
How many times can " 0" be reduced from '1' ?
Any number of times, and yet you will be always left with 1 to go on further isn't it ? That is why "infinity" !
Click to expand...
 
FrostedNipple said:
not on my calculator it isnt
hehe
Click to expand...
But your calculator is treating it as a number rather than a function. If you type in (Sin 0) / 0, it does Sin 0 = 0 and then tries to divide 0 by 0, which it can't do. Plot Sinx / x on a graphical calculator and see what it does.
 
Divide by zero is not defined. What you can say though is that if you look at the function 1/x, and take the limit as x --> 0, the function tends to infinity.

And for sin x /x, for small x, you can take sin x = x. So sin x/x does tend to 1.
 
Jokester said:
As far as I'm aware infinity is defined mathematically as any real number divided by zero.

Jokester
Click to expand...

I don't think that is correct. Mathemtically, division by zero is not defined.

sin(x)/x is NOT defined at x=0, but the limit x->0 does exist (from above and velow). If you take the function
Code: 
f(x)=sin(x)/x  for   x<>0
f(x)=1         for   x=0
it is continuous and differentiable and well defined and all the rest.
 
Last edited:
Amleto said:
I don't think that is correct. Mathemtically, division by zero is not defined.

sin(x)/x is NOT defined at x=0, but the limit x->0 does exist (from above and velow). If you take the function
Code: 
f(x)=sin(x)/x  for   x<>0
f(x)=1         for   x=0
it is continuous and differentiable and well defined and all the rest.
Click to expand...
Ok that makes sense.
 
Amleto said:
I don't think that is correct. Mathemtically, division by zero is not defined.

sin(x)/x is NOT defined at x=0, but the limit x->0 does exist (from above and velow). it is continuous and differentiable and well defined and all the rest.
Click to expand...

Yeah L'Hopital's rule gives you the limit. :)
 
Jokester said:
It's not defined as a real number, as inifinity isn't a real number.

Jokester
Click to expand...

Infinity is a defined concept though, and there are different 'types' or 'sizes' of infinity. For example, the total number of counting numbers (1,2,3 etc) is defined to be infinity (aleph-0), which is smaller than the total number of real numbers, which is also defined to be infinity (aleph-1).

Anything divided by zero is undefined.
 
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