This math argument just doesn’t add up

There’s a reason why this video pissed me off, but I’m not a math scholar and couldn’t explain it. Just the basic premise that if you add all positive numbers beginning with one, you’ll get a negative number is absurd.

The answer is infinity. Has to be. What bothered me is the guy pulled a trick by immediately going from 1+2+3+4+5+ …. = -1/12, and saying:

Rather than use these … let’s just think of this series.

No! Stop! That’s intentionally deceptive. If you’re making a case that 1+2+3+4+5+… = -1/12, use the numbers! Don’t use symbols. Using a different series is a red herring!

Well, that’s what I want to say. But as I said earlier, I’m not a math scholar, so I don’t have any defense for my argument because I don’t have the expertise.

Thank goodness for Mathbabe:

I’m not going to just vent about the cultural context, though, I’m going to mention what the actual mathematical object of study was in this video. Namely, it’s an argument that “prove” that we have the following identity:

“1 + 2 + 3 + 4 + … = -1/12.”

Wait, how can that be? Isn’t the left hand side positive and the right hand side negative?!

This mathematical argument is familiar to me – in fact it is very much along the lines of stuff we sometimes cover at the math summer program HCSSiM I teach at sometimes (see my notes from 2012 here). But in the case of HCSSiM, we do it quite differently. Specifically, we use it as a demonstration of flawed mathematical thinking. Then we take note and make sure we’re more careful in the future.

I feel better. Read Cathy O’Neal’s (Mathbabe’s) post here for the full counterargument. The headline: If it’s hocus pocus then it’s not math.


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