What is 1 divided by 0? Is it infinity?

Source: http://en.wikipedia.org/wiki/Division_by_zero

Contrary to popular opinion, 1 divided by 0 is not infinity! Wikipedia states that “the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so **division by zero is undefined**“.

## How to show that division by zero is undefined

$latex displaystyle lim_{xto 0^+} frac{1}{x}=+infty$

The limit of 1/x as x approaches zero from the right is positive infinity.

However, $latex displaystyle lim_{xto 0^-} frac{1}{x}=-infty$

The limit of 1/x as x approaches zero from the left is negative infinity.

Since the left limit and right limit are different, the limit of 1/x as x approaches infinity does not exist!

Note: There are mathematical structures in which *a*/0 is defined for some *a* (see Riemann sphere, real projective line, and section 4 for examples); however, such structures cannot satisfy every ordinary…

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March 28, 2014 at 5:08 pm

But for 1/x^2, the limit from both directions is positive infinity. So sometimes it makes sense to think of 1/0 as being infinity.

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March 30, 2014 at 6:49 am

Hello!! Thank you for sharing your thoughts. Many students would agree with you.

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March 30, 2014 at 11:15 am

I didn’t notice at first that this was reposted from another blog. I have left a longer explanation there.

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March 31, 2014 at 8:46 pm

Okay. Great!!

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