Considering the real number system..

[Ham]

If you look at the real number line, only in regards to rational numbers.

In other words.. if you plot every number that can be expressed as a ratio, or a fraction.. the line has more holes than it has numbers..

No wonder.. the first few pages of any math instruction book.. the instructors just quietly skip over..

No, you won't need that until the next class.. then one hears in the next class, no you really don't need that to do math until the next class.. then finally, one is in THE class. No wonder one can't figure what the hell the guy is trying to say at that point..

[Ham]

Why is the square root of two irrational? Is it really? Or do you just take my word for it?

Irrational means that it is IMPOSSIBLE to accurately describe this real world number in terms of the ratio of any two integers.

the number itself exists. one can produce it with a right triangle, with two legs of length one unit..

Don't get me even started on PI..

or e..

generally the proof involves assuming one can express an irrational number as the ratio of two integers, and logically arriving at a contradiction..

[Ham]

There is an old story about Pythagoras.. one of his students proved that the square root of two is irrational.

It is said that Pythagoras rewarded this student by strangulation. Others say he drowned him..

It's a very very old Greek urban legend.

[waysider]

Well, what do you expect from a discipline that's convinced pie are square?

Sheesh!

[Ham]

Kronecker was a dolt. He may have been brilliant at times, but he was otherwise a feeble idiot..

well, at least in my opinion.

He had too hard of a time, if any at all, thinking abstractly..

Cantor was really the beginning of brilliance, in the last (or was that the former) century..

[Ham]

So far I have not used any terms that anyone who has been through any high school math has not heard, or at least mostly understood..

rational numbers. any number, one can express as a ratio.. a/b, a and b are integers, or whole numbers. but b cannot be zero. can't divide by zero.

Real numbers. That is, numbers that can assume any value in real world situations.

Irrational numbers.. real numbers that cannot possibly be expressed as as a ratio..

[Ham]

that is.. well. Irrational numbers? Numbers one cannot express as a ratio of whole or integer numbers.. if one can convince oneself that they actually exist..

[Ham]

Math 119W is a math course, but it is communication intensive..

the students have to do some writing projects..

what do you think.. how about if a student wants to prove to the class that the square root of two is irrational..

would that qualify?

I would want a little bit of historical background..

it's not much. fifty points out of three hundred some..

it's not really that hard..

I mean.. there is loads of this on the internet somewhere, easy to access, easy to understand, easy to *copy*..

I know what is like to be a student..

copy, but carefully..

[Ham]

yeah..

well.. the last public proof that a mid-point convex function is convex, if we assume a continuous function, was entirely my own..

I don't know if it was entirely "right" or anything.. I've overcome the minor exception to my proof..

[Ham]

there was a general case that could be easily proved.. I didn't even come close to understanding it.. some general case of why it was so..

No thanks..

the professor said something like "I've never seen a legitimate proof.."

in that was another class, that I had not taken.

I think I at least partly blew his mind. Of sorts..

[waysider]

If 6 was 9, it would be music to my ears.

Heh!

[waysider]

What if you had

?

!

[Twinky]

Ham...

What've you been smoking? Or drinking??

Looks like you were having a nice little party by yourself last night!

[waysider]

Poly-rhythmic music defies the idea of mathematical exactness.....but it works. Edited August 25, 2012 by waysider

[johniam]

My 10th grade geometry teacher had a terrible cross to bear. Namely, her 4th hour class...us. There were more professional quality class clowns in that class than any other I've been in. Nobody tried to upstage anybody, it just flowed. Poor teacher.

She tried to teach us about the Pythagoreum theorum. One guy goes, "Huh? Puh FAG orus?"

Didn't Archimedes get his head chopped off by a soldier?