Help with problem

[jlind]

(08-13-2019 04:36 PM)Tonig00 Wrote:  I would likevto point out that is clearvthat 0/0 is undefined.
But any real number>0 divided by 0 I would say is infinite.

When we have a function in single variable I would say that if left an right limits are the same, then it is definite.

It may be the case of for example
5/(x-5)^2.

Tonig00,

Any number, divided by zero, is undefined.

• "Infinity" isn't a number, it's a concept. There's no such thing as Infinity+1, or Infinity*3 or Inifinity^2 being greater than Infinity.
• For any number, a <> 0, there is no number b for which 0 * b = a, which must exist by the definition of multiplication and division. 0 * b = 0, for any number b, but a <> 0. This is an impossibility.
  

This is why a / 0 is undefined. If it were "defined" as having some value, you would get endless fallacies like the following:
Let 1 = x
Multiply by x to get
x = x^2
Subtract 1 from each side to get
x - 1 = x^2 - 1
Divide both sides by x − 1 (this is a hidden division by zero as x = 1)
(x - 1) / (x - 1) = (x^2 - 1) / (x - 1)
1 = ((x - 1) * (x + 1)) / (x-1)
which simplifies to
1 = x + 1
Since x = 1, by substitution:
1 = 1 + 1, and therefore:
1 = 2

This is impossible. Hope this helps some with understanding why any number divided by zero is undefined.

John