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## Main Question or Discussion Point

I'm not sure where this would go specifically, mods move it to where you feel it needs to be if necessary.

I'm in a discussion with 2 guys about dividing by zero. I say its undefined and give the standard reasons why. They say it is. I'm pasting parts of the convo here and would like your input.

Me:

"All equations must be subject to reversiblity in some way. I know that isn't the official term.

8/4 = 2

can be re-expressed

2*4 = 8

8/0 = 0

cannot be re-expressed as

0 * 0 = 8"

Dude #1

"Actually, it does work:

8/0 = infinity -> 0 * (8/0) = infinity * 0 -> ( 0*8 )/0 = infinity * 0 -> 0/0 = 0 * infinity."

Me

"I disagree. And I'm not the only one.

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

http://mathforum.org/dr.math/faq/faq.divideby0.html

Here's a specific quote from the math forum website.

"But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

Does infinity - infinity = 0?

Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:

1 + (infinity - infinity) = 1 + 0 = 1, but

(1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero."

Perhaps elaborate on you reasons why?

Dude #2

"Mathmaticians are lazy," that is a direct quote from my Calculus professer.

Humans are imperfect, with imperfect minds, therefore we do not understand all levels of the true complexity of pure mathmatics, therefore the lazy mathmaticians who are dealing with these equations, unable to grasp infinity declare it "off limits" . (Math joke)

However in calculus if you do not know what a function is equal to at some number, you use the values you do know on either side and try to work close to the value you do not know, this is called taking the limit, if the equation seems to approach the same value when coming from either direction this value is the limit at this number. When taking the limt of 1/0 you find the function going to infinity from both directions, therefore the limit of 1/0 is infinty, the same as the limit of 4/2 is 2.

Now do you see why your calculator might display ERROR when you try this home,

you have the wrong calculator.

Dude#1

Discrete Mathematics and Calculus are two seperate branches of mathematics.

Discrete Mathematics, on which all computing machines, from pocket calculators to supercomputers are based, indeed does not allow for infinity at all.

Calculus, on the other hand, which has been essential to physics since Newton, deals infinities all the time and in that field 1/0 = infinity, and reciprocally, 1/infinity = 0.

Calculus does not provide for adding and subtracting infinities, only multiplying and dividing them, but in Quantum Physics, infinity - infinity does equal 0. This does violate the asociative property, but Quantum Physics is so strange anyway that it doesn't really matter.

I'm in a discussion with 2 guys about dividing by zero. I say its undefined and give the standard reasons why. They say it is. I'm pasting parts of the convo here and would like your input.

Me:

"All equations must be subject to reversiblity in some way. I know that isn't the official term.

8/4 = 2

can be re-expressed

2*4 = 8

8/0 = 0

cannot be re-expressed as

0 * 0 = 8"

Dude #1

"Actually, it does work:

8/0 = infinity -> 0 * (8/0) = infinity * 0 -> ( 0*8 )/0 = infinity * 0 -> 0/0 = 0 * infinity."

Me

"I disagree. And I'm not the only one.

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

http://mathforum.org/dr.math/faq/faq.divideby0.html

Here's a specific quote from the math forum website.

"But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

Does infinity - infinity = 0?

Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:

1 + (infinity - infinity) = 1 + 0 = 1, but

(1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero."

Perhaps elaborate on you reasons why?

Dude #2

"Mathmaticians are lazy," that is a direct quote from my Calculus professer.

Humans are imperfect, with imperfect minds, therefore we do not understand all levels of the true complexity of pure mathmatics, therefore the lazy mathmaticians who are dealing with these equations, unable to grasp infinity declare it "off limits" . (Math joke)

However in calculus if you do not know what a function is equal to at some number, you use the values you do know on either side and try to work close to the value you do not know, this is called taking the limit, if the equation seems to approach the same value when coming from either direction this value is the limit at this number. When taking the limt of 1/0 you find the function going to infinity from both directions, therefore the limit of 1/0 is infinty, the same as the limit of 4/2 is 2.

Now do you see why your calculator might display ERROR when you try this home,

you have the wrong calculator.

Dude#1

Discrete Mathematics and Calculus are two seperate branches of mathematics.

Discrete Mathematics, on which all computing machines, from pocket calculators to supercomputers are based, indeed does not allow for infinity at all.

Calculus, on the other hand, which has been essential to physics since Newton, deals infinities all the time and in that field 1/0 = infinity, and reciprocally, 1/infinity = 0.

Calculus does not provide for adding and subtracting infinities, only multiplying and dividing them, but in Quantum Physics, infinity - infinity does equal 0. This does violate the asociative property, but Quantum Physics is so strange anyway that it doesn't really matter.