please give some opinions

why can't we take any number divided by zero as a constant something like we do in the case of complex numbers

#Advice #Opinions

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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`	$\sum_{i=1}^3$
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Comments

You can't do it because multiplication by $0$ destroys information. That is, for $z = x \times y$ , $y \neq 0$ , we can recover $x$ via $\frac {z} {y}$ . However, when $y = 0$ , $0 = x \times y$ for all $x$ , so there's no way to recover $x$ through a division by $y$ --the information about $x$ has been destroyed. Anthropomorphically speaking, the division operator "doesn't know" what $x$ was-- $x$ could have been any number.

This isn't true of things like $i$ , since there's a reversal operation to recover what $i$ "used to be"--namely, squaring it.

It's possible you could put together a system of math where division by zero is defined in cases where you know the value of $x$ , since then you know how to reverse $x \times 0$ . That is, $z = x \times 0$ , and $\frac {z} {0} = x$ . I leave that as an exercise for the reader. :)

Christopher Johnson - 7 years, 9 months ago

That is a clear and charitable answer, Christopher. Thanks for doing this.

Silas Hundt Staff - 7 years, 9 months ago

Thanks;

Ajmal Ima - 7 years, 9 months ago

Umm ... $\dfrac{z}{0}$ is undefined (not a constant) for $z \in \mathbb{C}$ .

Jimmy Kariznov - 7 years, 9 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}`	$\boxed{123}$