Can you add past infinity? Find the fallacy in this video, if there is one.

## Adding Past Infinity (Warning: Math Ahead)

Posted by Maiu
on December 21, 2012

Posted by Maiu
on December 21, 2012

Can you add past infinity? Find the fallacy in this video, if there is one.

Hi Maiu,

I haven’t done calculus (yet), so I shouldn’t argue against those who have, but ….

Can you explain why it makes sense to use an infinite number of a different degree for the top series compared to the bottom? To my mind this is the only way the calculation works.

OK, I can concede that we’re talking about infinity, which isn’t real but a logical construct. For the calculation to work, it seems to me we need to have two different logical versions of infinity simultaneously, with one subtracted from the other in order to arrive at -1.

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Well, I think you got it (I don’t know to what extent, but you seem to grasp the main concept). The thing is he did infinity – infinity, which is undefined.

To properly understand why it doesn’t just cancel off (as the guy in the video thought it did), try reading the paradox of the wizard and the mermaid (it’s a bit long, but worthwhile) ðŸ™‚

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The problem started when he put down a divergent sum and multiplied it by 1 as if it was a number. Then he compounded the issue by treating it as a Real number.

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Why would you object to the result? It makes perfect sense. For example in 2-adic numbers, or as the value of the rational function 1/(1-x) at x=2.

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