Re: Calculus XOR Probability

cbrown@xxxxxxxxxxxxxxxxx said:
Tony Orlow wrote:
cbrown@xxxxxxxxxxxxxxxxx said:
Tony Orlow wrote:
cbrown@xxxxxxxxxxxxxxxxx said:
stephen@xxxxxxxxxx wrote:
cbrown@xxxxxxxxxxxxxxxxx wrote:

Well, one might then ask: why does he believe it in the finite case to
/start/ with? Because he read it in a book? Or because it can be proven
by a mathematical argument?

I thought about it in two ways.

First:

<actual proof snipped>

Second, list the naturals, in unary.
1
11
111
1111
11111
111111
......

See how it forms a diagonal half of a square?

No, I don't. Now what?

Cheers - Chas



So, no comment on the proof, and you don't see this array as being a square cut
diagonally in half.....never mind.

A proof is not a cajoling argument that depends on me "seeing"
something. A proof is a logical sequence of statements.

Why, then, did you say "actual proof snipped", and why do you deny that there
was a proof there to begin with? You can't comment on an inductive proof. Yes,
this goes nowhere like that.


If I write a program for a computer, and it contains a line of code
that reads "figure out the answer" the compiler stops: it's not a thing
that can be turned into a computer program.

That has nothing to do with the proof. If you cannot see that the list above
consitutes the growing diagonal half of a square, then you must have your eyes
closed. You ever try to teach a kid to tie his shoes? What would you say if
they asked, "what laces?". Probably walk away, right?


Similarly, if I encounter a statement such as "consider the function f:
N-> N defined by f(n) = n, see how it forms a diagonal half of a
square?", I may be able to /guess/ what you /might mean/ if we were
sitting in a bar talking, but it completely crashes my "proof
compiler": what you are providing is not a thing that can be turned
into a proof.

It's a visual proof. This axiomatic approach has taken a toll on human
understanding. There is more to life than symbols, or teaching dogs to paint.
If you can't see that it's the diagonal half of a square, then how do you
understand Cantor's diagonal arguments? You probably don't.


You need to turn the statement "see how it forms a diagonal?" into
something that is a mathematical statement, as opposed to one in
everyday English. Until then you haven't provided a proof; you've
provided a poem describing your thoughts on n*(n+1)/2.

This is why people hate math. When you learn to open your eyes to anything
besides a series of symbols, let me know.


Cheers - Chas



--
Smiles,

Tony
.

Relevant Pages

  • Re: Spot the missing tip.
    ... display uses more energy than a square inch of a square one? ... And a 4:3 is much closer to round the the riduculous 16:9 ... That's why our eyes are round too.. ... You quote an piece about energy efficiency and point ...
    (uk.legal)
  • Re: Great Cleave and Mirror Image
    ... > your eyes. ... with mirror images unless the wizard squeezes at least three images into ... pinpointed the right square (e.g., because all the figures are in one ... images versus spreading them out. ...
    (rec.games.frp.dnd)
  • Re: Blu-ray movies
    ... You see an image that is wider than it is high. ... When I use my eyes, I and everyone else has a certain focal point. ... anything except a square for a TV image a bad choice. ... purpose past scenery. ...
    (alt.tv.tech.hdtv)
  • Re: Blu-ray movies
    ... When I use my eyes, I and everyone else has a certain focal point. ... This alone makes anything except a square for a TV image a bad choice. ... purpose past scenery. ... I'll let my facts speak for me. ...
    (alt.tv.tech.hdtv)
  • Re: Powers of 2
    ... of minutes to write a computer program to search for the answer ... Let p be a prime which is one less than a square number. ... Since p is prime, it must be the case that n-1=1, otherwise, both n-1 and ... Dave ...
    (rec.puzzles)