This article about a teacher is really, really terrible, and sent Good Math, Bad Math blogger Mark Chu-Carroll into quite a tizzy. It is quite absurd, for basically all the reasons he mentioned, but the thing which I found most disturbing was how illiterate (innumerate?) the comments to this story were on the BBC blog.

One of the most egregious pet peeves: the claim that 1/0 is infinity. This is usually a sloppy restatement of saying that the limit of 1/x as x approaches zero is infinite, but 1/0 is simply undefined. if 1/0 was infinity, it implies that infinity times zero is one, which is, you must admit, a rather absurd result. It is important to realize that infinity (and nullity) are not numbers at all.

Some more absurd comments:

ItÂ´s all nonsense because instead of dividing ridiculous numbers people should better come together amd make different kind of stuff. Math is artifical (and boring), not real !

I love all the comments of people complaining that nullity is bull because it’s not on the numberline. Progress comes from thinking outside the box people

Unfortunately, some of the criticism is equally unfounded:

This idiot fails to recognize that anything divided by zero is infinity. We know this allready.

I am sorry Dr Anderson but “nullity” is the same as zero. Look at this; 0*0=0. Dividing by 0 on both sides and you get 0=0/0; zero = “nullity”. Or in words; 2 dolars to be divided equally between two persons, how much will each get? 2/2 = 1. 1 dolar to be divided between one person, how much will each get? 1/1 = 1. 0 dolar to be divided between zero persons, how much will each get? 0/0 = 0 (no one will get anything).

I’m not a mathematician. I fix and program and teach computers, and got into computer to get AWAY from higher math. This is probably flying high away in some ethereal, rarified height of mathematics us mere mortals never see and cannot appreciate. But it seems to me that yes, you can theoretically remove 0 from any given number an infinite number of times…. but if you’re removing 0, are you actually doing anything at all? I can, in theory, write an infinite number of $0.00 checks from my account and send them to everyone on Earth…. but all that would happen is my bank would get very vexed with me. Maybe there will someday be something to do with this wondrous new discovery, just as i is used in electronics somewhere. But until then I think this is just a bag of wind.

Dear Lord, I weep for the children. If my kid was in this guy’s math class, I think I’d go completely nuts. Some idiocy is so extreme I’d just have to punch him.

You can get a paper about this stuff here, and can see the curious idea that ∞^{-1} = 0 (axiom T69) which ultimately leads to the absurd result.

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