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Friday, September 02, 2016

Is This Right?

The following cute bit of humor is going about at the moment:



Hahahaha, as my daughters would text. Obviously, a really, really nerdy bit of humor, therefore right up my alley.

But here's the thing, I don't think the top one is fully correct.  For example, if I go to Wolfram Alpha and enter lim 1/(x-8) as x->8 it responds with "(two sided limit does not exist)" because you get infinity if you approach it from greater than 8 and decreasing and minus infinity if you approach it from less than 8 and increasing as shown in the following plot.



What do my nerdy readers think? Is it not quite right? Or is it okay? Is the default to always approach the limit from the positive side decreasing? Or from the side that gives you positive infinity? Or what?


15 comments:

Clovis e Adri said...

Nerds will be nerds.

A well defined formula would be achieved by x(+) -> 8 (where the '(+)' is meant as a subscript).

There is no default approach there, the specification is sure needed.

Now, as for the joke, I guess the anti-PC bit where it defines the student as a 'she' is subtle but certainly intentional...

erp said...

The symbol after the equal sign (=) in the top example is not the number eight (8) on its side as is the number five (5) in the second example.

I don't know why this is a joke?

Please explain for the batty old lady in group.

Bret said...

Clovis,

Hmmm. If it's "anti-PC" to say 'she' then that would be a sign PC has gone too far I think. Or maybe you're joking. 'Cause ya know, it is possible that it's a true or true-ish story and it happened to be a she who was the student. Or perhaps a trans-something-or-other. :-)

Bret said...

erp,

The main joke is that the student was apparently confused that the 8 on its side (∞), instead of representing infinity, was just a plain old 8 on its side. So when given a problem with 5s instead of 8s, she just put the 5 on its side for the answer and called it a day. So she learned a lesson, just the wrong one, even if clever in its own way.

What I think is kinda funny is that the example isn't quite fully specified (confirmed by Clovis above that one needs to specify the direction from which x approaches 8), so the tutor isn't doing a very good job tutoring and perhaps that's why she hasn't learned it correctly.

Clovis e Adri said...

Bret,

Many math/engineer jokes like that have a female character as the dumb student - that's an observation I have many years of data to back it up.

It is worth mentioning that, contrary to English (where "the" is used for both genders), in Portuguese you always need to specify gender ("a estudante" or "o estudante") so that's why I can tell you so. While you can do jokes in English without ever choosing the dumb student sex, you always make a choice in Portuguese.

I very much doubt it was a true story though.

Hey Skipper said...

Bret, going out on a limb here, if I recall correctly, infinity is not a number. If so, then isn't putting a sign in front of it a category mistake?

The number of primes less than zero is infinite, as is the number of primes greater than zero. If signing infinity was to have any meaning, then the sum of the quantity of primes is zero.

That's clearly wrong.

[Clovis:] Now, as for the joke, I guess the anti-PC bit where it defines the student as a 'she' is subtle but certainly intentional...

At the risk of getting shellacked by erp, IMHO, girls seem to not comprehend math as well as boys. My daughter did well in high school math, because she knuckled down and learned the rules.

Didn't understand a lick of it.

Just like there are men who are terrified of spiders, but very rare on the ground compared to women.

erp said...

Bret, yes, that's what I said -- the symbol in the top equation is not an 8 on its side. If one didn't understand that, then putting the 5 (or any other number) on its side in the second equation makes perfectly logical sense. Again, I don't get the joke and even Comrade Google couldn't explain it.

Skipper, don't go there. I was the only member of the superior sex in math classes all my life and I assure you many of those of the other sex (including my engineer brother) had lots of trouble with concepts, especially the engineering students who I think were more intuitive than math and physics students who loved the pure math, not the applications as did the engineers.

Room here for all god's creatures.

erp said...

... as for spiders, I was terrified of them before we moved to Florida, but here they are so pervasive and GIGANTIC -- as big as saucer, so if the old man isn't home, I deal with them myself. Pretty good for a city girl.

Hey Skipper said...

Back to my previous question, looked at differently.

[(x-8)^-1 | lim (-x -> 8)] + [(x-8)^-1 | lim (x -> 8)] = ?

Unless I'm missing something, just looking at the graph for both curves, the answer has to be zero.

So it matters, even if infinity is involved.

However, so far as I ever seen, the convention is that the absence of a sign means x is positive, and that's the tie breaker.

Clovis e Adri said...

Skipper,

You can easily prove (analitically) the above sum you wrote is zero.

There are different classes of infinity. For example, the number of integers is an infinite number, but it is still a lesser one than the infinite of real numbers.

But as long as you are writing ∞ and -(∞) in the same class, it is meaningful to write that they sum up to zero.


As for women in math, are you a collectivist now?

Hey Skipper said...

Clovis:

When I gave it a few moments thought it was obvious -- draw a line between every x and its corresponding minus x. They all pass through 0.

Is it true, that the absence of a sign means positive?

As for women in math, are you a collectivist now?

No -- equality of opportunity does not equal equality of outcome. There is a reason that joke only works with a female protagonist.

Just like any joke involving someone terrified of a spider isn't going to work if that someone is a guy.

And jokes involving incompetence with children will never work if the incompetent is a guy.

Humor is based in reality.

Clovis e Adri said...

Skipper,

---
Is it true, that the absence of a sign means positive?
---
It is not. Many people may take that as given, but every good Calculus textbook will advise about the importance of defining the limit direction.

That's even more important when you go to multivariable functions, where limits and derivatives are often direction dependent - and a bias towards 'limit by the right' makes no sense, since the limit may be from any direction of a N-dimensional space.

Clovis e Adri said...

Skipper,

---
There is a reason that joke only works with a female protagonist.
---

If there is, I don't get it. I would find it funny the other way too.

I am not trying to play the PC boring here, but in my experience at University level (where, to be fair, my sample is far from random), I see no relevant difference between genders.

I once had even the interesting case of a couple in same class (boyfriend and girlfriend) who were both the brightest students of their class (and of many classes ahead and before).

Yet she was better than him. I can swear to you she sometimes played a lower game in order to not embarass the boyfriend. It was really amusing.

The guy was mentored by me at undergrad level and is today on his path to a good academic career, AFAIK.

Hey Skipper said...

[Clovis:] I see no relevant difference between genders.

But do you see a difference in the quantity? My son is in his senior in Electrical Engineering. In his classes, women are extremely rare on the ground. Equality of opportunity and outcome are not the same.

---

Correcting what I wrote above: And jokes involving incompetence with children will never work if the incompetent is a woman.

I think that a safe bet, because I can't remember a single comedic situation involving incompetence with children, or just about anywhere in the house, where the protagonist isn't a man. Similarly, if there is to be a joke about somebody and tools or fixing something, then that somebody is likely to be a woman (except, of course, for the long standing US sitcom tradition that if a joke relies upon somebody doing something incompetent, foolish or stupid, it is always a man doing it).

For comedy to work, it has to be based on shared experience and expectations. Yes, I am sure that there are women who are good at math, but I would bet that in most people's experiences most girls and women do not like math, unless they absolutely hate it. So a joke involving mathematical incomprehension (or parallel parking) is more likely to have a female.

Clovis e Adri said...

Skipper,

Sure there is a difference in quantity in Physics and Engineering.

But, quite the "paradox", it is not difficult to see classes majoring in Mathematics where women are in equal or greater numbers.

Most of them will go to be school teachers, instead of following research, though. Which explains the gap you see among the professors of a Math department.