## Tired Math

Posted March 9th, 2004 @ 04:12pm by Erik J. Barzeski

My brain has unusual thought patterns when I'm tired. Today, for example, after I got my speeding ticket I remembered that 0-15 MPH over the speeding limit gets you 3 points, but 15-30 (I think) gets you 4. 15, you'll note, is included twice, but it'd be rather inaccurate to say "16-30" because then if you were going 15.63 MPH, you'd get off scott free (unless you round).

I began to think of people who'd whine about their grades, saying that an "89.6" is the same as a "90" and that they should get an A, while my stance has always been "nope, you fell short, by probably at least one question somewhere during the course of the class."

So, I came up with the idea that the rules should say "0 to 15 MPH" for a 3-point offense and then "15 + 1/infinity to 30 MPH" for a 4-point offense. After all, 1/infinity seems to be the smallest possible increment, right? But is it the same as zero? Does 1/infinity = 0? I don't suppose that it does - it has *some* value, does it not?

Consider that 1/9 = 0.11, 2/9 = 0.22… 7/9 = 0.77, and 8/9 = 0.88 (all of those repeat infinitely).

Does it not follow that 9/9 would equal 0.99?? And if 0.99 is the same as 1 (because 9/9 is 1), then is 1/infinity equal to zero?

I don't know. And frankly, I'm too tired to care. π

P.S. Here's a bad joke. What's the square root of 69? Eight something. Get it? π

Posted 09 Mar 2004 at 4:18pm #Since 9/9 = 0.9999999999999, and 9/9 = 1, and 9/9 - 1 = 0, then 9/9 + 1/inf = 1, and 1/inf = 0.

I'm obviously still tired.

Posted 09 Mar 2004 at 4:22pm #In calculus we did the 1/infinity a few ways. With infinite series, you can actually sum up the volume of the graph. For most purposes (limits for instance), it's 0.

Posted 09 Mar 2004 at 4:44pm #mathematicians would probably say that 1/infinity is a real number (although infinitesimal by definition) because otherwise you can't sum infinitesimal numbers (take an integral). All my engineering classes say that it's close enough for practical purposes.

Posted 09 Mar 2004 at 6:26pm #Jo-Pete, hmm, reminds me of a joke:

A mathematician, a physicist, and an engineer were asked to review this mathematical problem. In a high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. The mathematician, physicist, and engineer were asked, " When will the girls and boys meet?" The mathematician said, " Never." The physicist said, " In an infinite amount of time." The engineer said, " Well... in about two minutes, they'll be close enough for all practical purposes."

Posted 09 Mar 2004 at 6:35pm #saying that an "89.6" is the same as a "90"I wish my school did it like that, with a 90 being an A. Currently a 93 is the lowest A you can get. Argh.

Posted 09 Mar 2004 at 6:55pm #My college did 90/80/70/60. My high school did 93/86/75/68. I liked my high school's grading scale far more. It allowed me to separate myself from the people who could manage to get a 91 consistently. π

Posted 09 Mar 2004 at 8:35pm #This reminds me of the beginning of every Real Analysis "joke" ever told:

"First, assume epsilon greater than zero..."

Posted 09 Mar 2004 at 9:52pm #Yet another (bad) math joke:

A constant and e to the x are walking down the road when they see a derivative approaching. Upon seeing the derivative the constant screams, "I'm surely a goner!" e to the x calmly replies, "I have nothing to fear." As the derivative gets closer, the constant runs away in terror. e to the x calls out to the derivative, "you do not scare me!" When the derivative finally reaches e to the x, he extends his hand and says, "Hello I'm d/dt".

Posted 09 Mar 2004 at 10:21pm #0.999... (repeating an infinite amount of times) does in fact represent the same value as 1

Posted 10 Mar 2004 at 12:57am #1/infinity is not actually a real number. It's what's called a hyperreal number, which is a superset of the real numbers. There's an infinite number of hyperreal numbers between each real number, which is something that's hard to grok.

So no, 1/infinity != 0. Zero is a real number, and 1/infinity is the hyperreal number right about zero.

Posted 10 Mar 2004 at 3:23am #There's an infinite amount of

realnumbers between any two real numbers, so that shouldn't surprise anyone.Posted 10 Mar 2004 at 1:18pm #1/inf is indeterminate.

At most you can say:

\lim x -> \inf 1/x = 0

This is all calculus. For some free calculus texts see a recent Slashdot story: http://books.slashdot.org/books/04/03/04/028253.shtml

Posted 11 Mar 2004 at 4:56pm #So, what did you get your ticket for? How fast were you going?

Posted 24 Mar 2004 at 11:21pm #Actually you can prove that .99999... is in fact 1 using an infinite series:

since this can be represented as the geometric series:

9/10 * (1 + 1/10 + 1/100 + 1/1000 + ...)

The formula for calculating an infinite series is:

a/(1-r)

where: a is the first item in the series and r is the rate of change.

9/10 is the first number and 1/10 is the rate of change.

Therefore:

(9/10)/(1-1/10) = (9/10)/(9/10) = 1

Q.E.D.