# Number must be zero

1. Nov 12, 2015

### gokhul

Let N be any number
N÷∞=0
Cross multiplying
N=0*∞
Any number multiplied by zero is zero
Even infinity is a number but it is large
So
N = 0

2. Nov 12, 2015

### gokhul

Is my assumption correct

3. Nov 12, 2015

### DaveC426913

No.

You cannot perform arithmetic operations on infinity.

More particularly, N÷∞= undefined.

4. Nov 12, 2015

### Staff: Mentor

Infinity is not a number. You can't use it like that.
$$\lim_{x \rightarrow \infty} \frac{N}{x} = 0$$
$\lim_{x \rightarrow \infty} 0 \times x$ is undefined.

Correction: $0 \times \infty$ is undefined.

Last edited: Nov 12, 2015
5. Nov 12, 2015

### Staff: Mentor

You assume that you can handle zero and infinity as numbers. As been said infinity isn't a number. 0 is a number but it doesn't belong to the halfgroup of ℕ or ℤ or group of ℚ or ℝ or ℂ with multiplication as group operation. It simply does not exist in there and therefore cannot be multiplicatively inverted.

Last edited: Nov 12, 2015
6. Nov 12, 2015

### jbriggs444

[Edit: removed quote of Dr. Claude's original]

$\lim_{x \rightarrow \infty} 0 \times x$ is defined and is equal to zero. However, that does not mean that $0 \times \infty$ is defined.

Last edited: Nov 12, 2015
7. Nov 12, 2015

### Staff: Mentor

Yes. That was botched cut and paste. Thanks.

8. Nov 12, 2015

### LAZYANGEL

Infinity and the infinitesimal cannot be treated as straight up values for arithmetic operations, infinity is not a number you can reach. Defined by the limit as values for x gets bigger and bigger in contrast with constants in the expression. Just like what DrClaude said.