Zero

Originally posted by TheMaster37
I don't, physisists do.
....
What is the limit of x approaching 0 of 1/x?

Correct answer; it has no limit. Though often one says that the limit is infinity. If you calculate 1/x for small x, you'll never get to infinity.

Your terminology is completely Wrong.

Limit x = 0
x~0

Limit (1/x) = increases without bound
x~0+

Limit (1/x) = decreases without bound
x~0-

Limit (1/x) = Does not exist by reason of divergence.
x~0

Let me clarify my statements then.

The only way I know to evaluate an expression where zero is a dividend is to use limits.

If the expression evaluates to k/0 where k is non-zero, the expression might either diverge (1/x), or the limit as both sides approach the key value might both increase or decrease without bound, in which case I would tentatively say that the expression has the value of either positive or negative infinity, depending on the case

Now this goes beyond the realm of real numbers and hence has no meaning in normal algebra. As such, I would deem this discussion would fall under a branch of mathematics which deals with infinite numbers, of which I know little, except that there may be several systems of though, including one where positive infinity is equal to negative infinity (which would make functions such as 1/x and tan x contiguous across those points within that branch.)

However, an expression which evaluates to 0/0 is a slightly different story. Using limits as before, you may find that it approaches a finite value from both sides, or it may behave as k/0, depending on the relationship of the numerator to the denominator.

For the purpose of real number mathematics though, expressions with division by zero don't have a value.

a = b = 1

=> a^2 = ab

=> a^2 - b^2 = ab - b^2

=> (a+b)(a-b) = b(a - b)

=> a +b = b

Therefore 1 = 0

Originally posted by DeepThought
a = b = 1

=> a^2 = ab

=> a^2 - b^2 = ab - b^2

=> (a+b)(a-b) = b(a - b)

=> a +b = b

Therefore 1 = 0

Hey, you divided by 0, that's illegal! If a=b=1, than a-b=1-1=0.

Originally posted by kbaumen
Hey, you divided by 0, that's illegal!

Arrest me then.

Let's assume for a moment that 0/0 has a value.

We try to find the limit f(x) when x approaches zero in two cases:
(1) When f(x) = x/x. The limit is of course 1, so 0/0 = 1. Right?
(2) When f(x) = 0/x. The limit is of course 0, so 0/0 = 0. Right?
Now I have proven that 0 = 1. Right?

Wrong! Why? Becuse you cannot ever evaluate 0/0, in fact no division by zero. Never. It's not possible in any number system, not in R, not in Q, not in C, not ever.

Please, give up your efforts to try to divide by zero. It is well proven that it's not possible.

Originally posted by FabianFnas
Let's assume for a moment that 0/0 has a value.

We try to find the limit f(x) when x approaches zero in two cases:
(1) When f(x) = x/x. The limit is of course 1, so 0/0 = 1. Right?
(2) When f(x) = 0/x. The limit is of course 0, so 0/0 = 0. Right?
Now I have proven that 0 = 1. Right?

Wrong! Why? Becuse you cannot ever evaluate 0/0, in fact no divi ...[text shortened]... ase, give up your efforts to try to divide by zero. It is well proven that it's not possible.

The "proof" I gave above is an old paradox meant for amusement. Anyway why are you arguing with it, if 1 = 0 then by iteration all numbers are equal and you have the same rating as Anand.

Originally posted by DeepThought
The "proof" I gave above is an old paradox meant for amusement. Anyway why are you arguing with it, if 1 = 0 then by iteration all numbers are equal and you have the same rating as Anand.

Nah, my last posting was only a new posting with another twist than before. It wasn't meant to be an answer to yours.

Some says that it is possible to divide by zero, I say no it isn't, that's all.

Originally posted by FabianFnas
Nah, my last posting was only a new posting with another twist than before. It wasn't meant to be an answer to yours.

Some says that it is possible to divide by zero, I say no it isn't, that's all.

My mistake 🙂

It is possible to divide by zero, it's just that you shouldn't expect to get a meaningful answer...