I am confused

$\frac{1}{0}$ = $∞$

My teacher says this is undefined, while my calculator says this is true. Is this true or false?

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Any number divided by zero is undefined.

Monishwaran Maheswaran - 4 years, 11 months ago

Your calculator will simply say whatever the programmers of said calculator told it to say for division by 0. Mathematically speaking though, division by 0 is undefined.

M K - 4 years, 11 months ago

Then why does the limit of 1/x as x approaches 0 approach $∞$ ?

alex wang - 4 years, 11 months ago

The limit of 1/x does indeed approach ∞ as x approaches 0+. (0+ meaning the positive side of the x-axis). That being said, it also has another limit: -∞, as x approaches 0-. (0- meaning from the negative side of the x-axis). This means that there are two limits of the function 1/x, and on extension, 1/0. Both ∞, and -∞. Since there is no single limit, it is undefined.

M K - 4 years, 10 months ago

You first need to know that infinity is not a number. It doesn't follow simple algebra. Infinity is largest term that we cannot approach. Infinity depends on one's point of view to define.

Dev Rajyaguru - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$