Search found 833 matches

by wtf
Fri Oct 09, 2015 1:08 am
Forum: Articles in Philosophy Now
Topic: Would My Zen Master Fail Me For Writing This Article?
Replies: 1
Views: 574

Re: Would My Zen Master Fail Me For Writing This Article?

"This article is available to subscribers only."

I have let go of my attachment to reading it.

The Tao you can subscribe to is not the true Tao. Or so I've heard.
by wtf
Fri Oct 02, 2015 11:17 pm
Forum: Logic and Philosophy of Mathematics
Topic: Axioms and postulates
Replies: 5
Views: 1058

Re: Axioms and postulates

if there was a difference a couple of thousand years ago, there isn't today. And an axiom is no longer something that we see is true by observation. Rather, it's a statement accepted without proof in order to get a particular deductive system off the ground. The standard axiomatic system for all mat...
by wtf
Tue Sep 29, 2015 12:36 am
Forum: Logic and Philosophy of Mathematics
Topic: Comparing infinite sets
Replies: 5
Views: 1779

Re: Comparing infinite sets

It occurs to me that I owe a much more clear explanation of the chain of cardinal arithmetic showing that the set of curves in the plane has the same cardinality as the real numbers. I shall do this now. There are three things we need to know. 1) If X and Y are sets, the set of functions from Y to X...
by wtf
Mon Sep 28, 2015 8:12 pm
Forum: Logic and Philosophy of Mathematics
Topic: Comparing infinite sets
Replies: 5
Views: 1779

Re: Comparing infinite sets

This is my second in a series of posts reviving @PhilX's old posts on infinity in order to clarify some issues of philosophical interest and importance. The first thread in this series is http://forum.philosophynow.org/viewtopic.php?f=26&t=15446, and it wouldn't hurt to read that one first if you ha...
by wtf
Fri Sep 11, 2015 5:19 am
Forum: Logic and Philosophy of Mathematics
Topic: Proving that the difference between any two anagram numbers is always a multiple of nine
Replies: 59
Views: 5927

Re: Proving that the difference between any two anagram numbers is always a multiple of nine

Here's the proof that the difference of anagrams is divisible by 9. First, note that x = x0 + x1 * 10 + x2 * 10^2 + ... + xn * 10^n (writing xn or sometimes x_n to mean "x_subscript_n") and likewise y = y0 + y1 * 10 + y2 * 10^2 + ... + yn * 10^n. Note that since the x_i's are just a rearrangement of...
by wtf
Thu Sep 10, 2015 12:22 am
Forum: Logic and Philosophy of Mathematics
Topic: Is infinity all black and white?
Replies: 5
Views: 1103

Re: Is infinity all black and white?

@PhilX, I resurrected this months-old thread because you have a lot of similar questions about transfinite cardinals in this and other threads and I wanted to unpack some of these issues if you're still interested. The question of whether every infinite set is cardinally equivalent to an Aleph is ac...
by wtf
Tue Sep 08, 2015 11:54 pm
Forum: Logic and Philosophy of Mathematics
Topic: Differential calculus defined by differences - what more meaningful ?
Replies: 12
Views: 1456

Re: Differential calculus defined by differences - what more meaningful ?

A quick Google search will show that this author is a well-known crank. Regarding calculus, he clearly has never seen the proper formalization of the concept of a limit. He has an Amazon book if anyone wants to send him money.
by wtf
Tue Sep 08, 2015 11:43 pm
Forum: Logic and Philosophy of Mathematics
Topic: Does the center of a disk exist?
Replies: 22
Views: 3170

Re: Does the center of a disk exist?

a) Case of a physical disk. You can't precisely find or define the center to arbitrary precision because of measurement error. And any physical rotational mechanism is imperfect and has some amount of wobble. So there is no stationary point in a physical spinning disk. b) Case of a mathematical disk...