Thread: Steven's Trilogy - Zero Equals Infinity

Originally Posted by Naiya

According to my physics professors, dividing by zero equals infinity. Now feel your brain explode as mine did.

Uh oh, I am going to have to argue with your professors. Dividing by zero does not result in infinity. Dividing by zero is impossible.

8 divided by 2 is 4 because 4 is what you multiply 2 by to get 8. Now imagine 5 divided by 0. 0 times what equals 5? There is no answer. Even infinity does not work.

Originally Posted by Universal Mind

Uh oh, I am going to have to argue with your professors. Dividing by zero does not result in infinity. Dividing by zero is impossible.

8 divided by 2 is 4 because 4 is what you multiply 2 by to get 8. Now imagine 5 divided by 0. 0 times what equals 5? There is no answer. Even infinity does not work.

Bullshit.

If you have the function f(x) = (2+x)/(3-x) then what is the limit as x --> 3^-?

x/0 is an infinitely large number.

For x =/= 0

Pay attention as I blow your mind with my algebra skills:

x/0 = ∞

x = 0·∞

x/∞ = 0

As any nonzero number divided by infinity is infinitely small, the only solution is 0. Apply the inverse and you arrive at infinity.

You overlooked a problem with your big mind blower. Infinity is not a number.

http://mathforum.org/dr.math/faq/faq.large.numbers.html

http://nrich.maths.org/2756

It is impossible to divide by zero, at least in terms of real numbers.

http://www.math.utah.edu/~pa/math/0by0.html

http://en.wikipedia.org/wiki/Division_by_zero

Well of course it's not a number. However the limit still exists and it is still infinity.

The function I gave has a limit as x --> 3^-. It is an undefined number, or infinity.

'Infinity' is an expression of the lack of a limit though.

I think the key point is that the limit of a function towards a number doesn't imply things about the function at the number. The question is 'what is 1/0'; the fact that the limit of 1/x as x tends to 0 is infinity does not imply that 1/0 is infinity.

The problem with such a statement is clear if you consider what happens when you take the limit in different directions; you get plus and minus infinity. They can't both be the value of 1/0.

Why not? Both require infinitely large numbers to "work". Just as dividing any constant by infinity is basically zero as the result is "infinitely" small, the only number which would work is 0.

At your last point; that depends on the function. f(x) = (3)/(3-x)² has a 'limit' at 3.

But dividing any c by minus infinity would also be 0, so c/0 = -infinity

1/0 can't be two different things. Then division would no longer be an operation.

f(x) = (3)/(3-x)2 still doesn't have a value at 3 because as I've explained limits don't imply things about functions at the limit.

If you have the function f(x) = (2+x)/(3-x) then what is the limit as x --> 3-?

You have to be careful though, firstly because the whole point is that there isn't a limit, and secondly because the existence of the limit doesn't imply anything about the function at the actual value.

For example f(x) = 1 when x = 0, 0 elsewhere. The limit of f(x) as x tends to 0 is 0, but f(0) is 1.

As a matter of fact, if and only if the limit of f(x) as x tends to 0 is f(0), the function is continuous; so the example function you gave isn't.

Originally Posted by Universal Mind

Uh oh, I am going to have to argue with your professors. Dividing by zero does not result in infinity. Dividing by zero is impossible.

8 divided by 2 is 4 because 4 is what you multiply 2 by to get 8. Now imagine 5 divided by 0. 0 times what equals 5? There is no answer. Even infinity does not work.

Well, THER'S YER PROBLEM.

You're using math logic. Allow me to give the full version of the story. I was measuring the resistance of different parts of an electric circuit and had just made a pretty shiny graph showing my data in Excel. When the professor walks by we ask him if it looks all right. He said, "well, what happens when you divide by zero?"

"The universe explodes!" said I.

"You can't divide by zero!" said my lab partner.

"This isn't a math class! In physics a division by zero is infinity."


So our diode had infinite resistance at certain voltages according to the graph.

The end!

Originally Posted by Naiya

Well, THER'S YER PROBLEM.

You're using math logic. Allow me to give the full version of the story. I was measuring the resistance of different parts of an electric circuit and had just made a pretty shiny graph showing my data in Excel. When the professor walks by we ask him if it looks all right. He said, "well, what happens when you divide by zero?"

"The universe explodes!" said I.

"You can't divide by zero!" said my lab partner.

"This isn't a math class! In physics a division by zero is infinity."


So our diode had infinite resistance at certain voltages according to the graph.

The end!