Note to self: math is weird

[smlvalentine]

I’m not going to lie to you: having taken Calculus 2 and passed (with the A? We’ll find out on Monday) I’m still uncertain if I understand the damn stuff. However, having used some of it today, I feel pretty proud

Comments

[tekunokurato]

sam what

the stupid race paradox has the logical problem that it doesn't proceed to the conclusion of the race but only measures up to where the race approaches T=1, which is stupid

I hate zeno and when people use his stupid paradoxes

and I don't get the math, but presumably I'm just un-smart, so it's okay

[smlvalentine]

Haha, I love how you focus on the least important detail of the article (though I assume your ire is directed at Zeno and not myself regardless of the "sam what.")

In any case, the math here is actually quite simple; I'm terribly sloppy.

Without going into too many details of sequences, geometric sequences (which can be depicted as the sum of the first number in the sequence multiplied by a constant value which is, itself, raised to an "n" power; sigma (from 0 to infinity) of a*r^n.)

So, in the case of .9999... the first number of the sequence is .9, the constant by which it is multiplied to achieve the next number in the sequence is .1 (ad infinitum) and "n" is simply a placeholder for the level of the sequence.

The fun begins when you're told that the point of convergence for a geometric sequence is (a)/(1-r) which I've depicted above as .9/(1-.1) which is, of course, 1.

Assuming that's all coherent, cool huh?

[tekunokurato]

Yeah, I know it's the least important part; it's just that I can't believe nobody slapped him around when he originally said it. I bet he was some kind of academic comedian that was just basically telling jokes (like that economist comedian with the youtube vid), and somebody wrote one down, then we found it like four hundred years later and thought it was some great greek revelation (people were extremely stupid 400 years after zeno lived).

Anyway, I don't know what the point of convergence is and google wasn't helping me, so I gave up (I did understand it up until that point, but I just note that the obvious logical fallacy if there is one is that phrase that I don't actually understand). whatevs

[tekunokurato]

okay okay so I get it. for me the more interesting point is, as wikipedia phrases it, "every non-zero, terminating decimal has a twin with trailing 9s."

but I also can't frankly see why this is wrong: "Some students regard 0.999… as having a fixed value which is less than 1 by an infinitely small amount."

haha, okay, after reading the "Of the elementary proofs, multiplying 0.333… = 1⁄3 by 3 is apparently a successful strategy for convincing reluctant students that 0.999… = 1." I am indeed more convinced, because that's "intuitively" 100% correct.

But really what we're saying is that, in the same way that 1/3 is a convenient way to not have to show .3333[repeating], 1 is merely another way of representing .9999999, or that ANY rational number is merely another way of expressing its crazy-talk counterpart. IT BLOWS YOUR MIND