Problem To Do For Fun

Algebra Level 1

What is 10÷0?

undefined 10 0

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2 solutions

Garam O'Brien
Feb 9, 2019

If 10/2 (which is five) is multiplied by two, it becomes 10, the previous numerator. Same with any other fraction where a number is divided by a number, x, and once again multiplied by x. In this case, if 10/0 is multiplied by 0, it should be ten according to the rule I previously stated, however, another rule also states that anything multiplied by 0 is 0. Therefore, it is undefined.

Jordan Cahn
Jan 9, 2019

Depending on the context in which the problem arises, 10 0 = \frac{10}{0}=\infty may be a valid answer.

No not consistent since you took the limit as x approaches 0 from the left. If you took the limit from the right, you approach -\infty . So the answer must be undefined.

Hans Gabriel Daduya - 2 years, 5 months ago

That's assuming 10 0 \frac{10}{0} arises from lim x 0 10 x \lim\limits_{x\to0}\frac{10}{x} . Which indeed would mean the limit wouldn't exist.

However, there are other contexts in which it could arise. For example, lim x 10 x 2 = 0 \lim\limits_{x\to\infty}\frac{10}{x^2}=0 . Additionally, we don't even need a limit. If we're dealing with the real projective line (which adds a formally-defined "point at infinity") we don't even need a limit to write 10 = 0 \frac{10}{\infty} = 0 .

Jordan Cahn - 2 years, 5 months ago

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