Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2007-07-18 08:52:36

Identity
Member
Registered: 2007-04-18
Posts: 934

m/0 = ∞?

Is it true that

m≠0?  I've heard many say it's true. However, any number divided by 0 will surely give a result "greater" than inifinity, because even an infinite number of 0s could not make m, and hence 'undefined'.

The question came to me while looking at this unintentionally funny proof of god:
You know the formula, m over nought equals infinity, m
being any positive number? Well, why not reduce the
equation to a simpler form by multiplying both sides by
nought. In which case you have m equals infinity times
nought. That is to say that a positive number is the product
of zero and infinity. Doesn't that demonstrate the
creation of the universe by an infinite power out of nothing?
Doesn't it?
tongue

Offline

#2 2007-07-18 09:33:36

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: m/0 = ∞?

This is simply by definition of what we mean by "divide", which is "multiply by the inverse of b".

So the question is, what is 0-¹.  In general, we have a-¹ is a number such that:

a * a-¹ = 1

Thus, the question becomes what number k is there such that:

0 * k = 1

And of course, the answer is that such a number doesn't exist.  So the question of dividing by 0 doesn't even make sense.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

#3 2007-07-20 00:14:11

HallsofIvy
Guest

Re: m/0 = ∞?

Identity wrote:

Is it true that

m≠0?  I've heard many say it's true. However, any number divided by 0 will surely give a result "greater" than inifinity, because even an infinite number of 0s could not make m, and hence 'undefined'.

The question came to me while looking at this unintentionally funny proof of god:
You know the formula, m over nought equals infinity, m
being any positive number? Well, why not reduce the
equation to a simpler form by multiplying both sides by
nought. In which case you have m equals infinity times
nought. That is to say that a positive number is the product
of zero and infinity. Doesn't that demonstrate the
creation of the universe by an infinite power out of nothing?
Doesn't it?
tongue

No, it is not true.  "infinity" is not a number. 

is not anything- it is "undefined".

Latex fixed - Ricky

Board footer

Powered by FluxBB