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# 146

How To Make A Mathematician Angry - January 16, 2010
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I don’t get it. :( The 4/9N-2/3 looks very arbitrary but I don’t see a reason for a mathematician to cringe because of it. Please explain.

It makes a mathematician cringe because it switches the standard use of epsilons and Ns. Usually, to prove convergence of stuff(n) to L as n approaches infinity , you must prove that for every e>0, there exists N such that for every n>N, |stuff - L|<e. (e is epsilon here)
If you switch the roles of epsilon and N in the proof, it will take ages to understand you.

Correction to previous post: You must prove that |stuff(n) - L| < e.

Wait, what the hell, it doesn't display the "less than" sign, and deleted the "e" to its right. That's weird.
It wrote |stuff(n) - L| less than e.

Ya, that's annoying haha. I changed it to use the html code for < so it shows up in your entry now.

ODDin: someone probably figured removing everything that might remotely look like dangerous HTML tags is safer than escaping it :)

I'm a mathematician and it doesn't make me cringe. It makes me burn with curiosity for Spiked Math's next line of the argument...

I don't know--I didn't like Calculus proofs that much anyway...Number Theory was much more fun.

Cringe.

Does it really mathematician cringe? Maybe if you call calculus mathematics.. :))

Well, a further problem is that we get negative epsilon0 for natural N. This is really disgusting!

By the way, you can show it trivially with l'Hôpital, since both, d(2n)/dn = 2 and d(3n+2)/dn = 3 exist. The fraction of these is 2/3, as claimed.

l'hopital is overkill... just multiply both sides by 1/n and use that 1/n -> 0 as n->oo. i think this one is kind of lame, unless there's some great punchline that i'm missing

Well, if you want a formal prove you have to show that each of the limes exist, which is more work to write down, I think. Either way, the problem is trivial; The joke is the unconventional (=bad) use of epsilon and N and the fact, that epsilon is not necessarily positive.

If an epsilon is a hero,
Just because it is greater than zero,
It must be mighty discouragin'
To lie to the left of the origin.

This rank discrimination is not for us,
We must fight for an enlightened calculus,
Where epsilons all, both minus and plus,
Have deltas
To call their own.

http://www.haverford.edu/physics/songs/lehrer/delta.htm

um... so I'm in an algebra 2 class. I get most of these jokes but this epsilon thing contiues to allude me, which is anoying because I see it all over the place. Could someone explain it to me

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