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What is 1 divided by 0?


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What is 1 divided by 0? Is it infinity?


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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Author: Math Education Concepts

I am a Co-founder of Excel Philly, Inc. (Math Corps Philadelphia). I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I have a passion for Mathematics Education, especially in urban communities.

4 thoughts on “What is 1 divided by 0?

  1. 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.


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


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