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1/0 = H

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Location: Oregon

PostPosted: Sun Sep 21, 2008 10:20 pm    Post subject: 1/0 = H Reply with quote

Time Clock wrote:
...0/1 is zero. Therefore 1/0 (infinity) X 0/1(zero) = 1.

I find it pretty strange that you should mention this.

It's been years since I've thought about this, but I did something
much along these lines, also in high school. I defined 1/0 as H.

Maybe more people than I imagine have investigated these ideas.
Looking back on it, I can see that I was being taught abstract
algebras (groups, rings, etc.) and complex numbers (4 + 5i)
around the same time. It seemed natural to invent a new unit.

To say my enthusiasm for this new unit was not widely shared
would be accurate, though there were a few that
humored me. It would be fun to weave a story out of how it might
have played out, ending in a rant about those mathematics
teachers desperately attempting to protect their precious
Abelian Groups from any source of internal inconsistency.
I embrace nearly every opportunity to say "They laughed at me
at the Academy."

But the truth is, the implicit algebra underlying H (and also your
formulation), doesn't have much utility. Still, I had fun with it.

For example:
H+H = 2H
H + 1 = H

and, as you note: H * 1/H = 1
or, alternately, H * inv(H) = 1

If I recall correctly, I thought H * 0 = 0, which leads to a clear
inconsistency, unlese 0 is not equal to 1/H.
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