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# Is 1/0 infinity?

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Is 1/0 infinity?

I've been shown a "proof" against this that assumed infinity is equal to 0 to prove that infinity is not 1/0, and I found that to be absolutely absurd. I guess the REAL question is this: "Is the statement 1/0=infinity paradoxical if we have no prior knowledge of what infinity is?" In this sense, infinity could be any type of value, such as Prime, Perfect Square, Negative, Imaginary, Irrational...you get it, right? I'm not defining infinity as anything other than 1/0, so if you find that to be paradoxical, please prove within the bounds of "We know nothing about infinity yet other than it's the reciprocal of 0."

Thanks for the help!

Feb 3, 2020

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Feb 3, 2020
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Here is the graph of y=1/x

You can see that as x approaches 0 from the positive side, 1/x approaches infinity.

But

you can also see that as x approaches 0 from the negative side 1/x approaches -infinity.

Therefore  1/0  is undefined.

Feb 3, 2020
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"In this sense, infinity could be any type of value..."

Right there is a fundamental error.  Infinity can not be treated as a value.

Feb 4, 2020