# Re: TM Tape is Always Finite

From: Thomas Bushnell, BSG (tb+usenet_at_becket.net)
Date: 01/03/04

• Next message: Pinaki Mitra: "Re: Complexity of computing normal subgroup"

```Date: 02 Jan 2004 21:44:29 -0800

```

"Arthur J. O'Dwyer" <ajo@nospam.andrew.cmu.edu> writes:

> I can easily understand how some people don't "get" infinity. I
> myself still don't quite "get" ordinal numbers, although I've got
> the cardinals down pretty well now. :)

Eek. I find the ordinals far more comprehensible than cardinals;
maybe I've done too much set theory.

Thomas

• Next message: Pinaki Mitra: "Re: Complexity of computing normal subgroup"

## Relevant Pages

• Pure-cardinal approach *is* possible! (was: Mathematical concepts)
... Your ordinals start with zeroth, not first, right? ... So cardinals are defined, in terms of sets of ordinals, like ... For example if you think of your head, your hands, suits ... there's a gap between hands and suits. ...
(sci.math)
• Re: Pure-cardinal approach *is* possible! (was: Mathematical concepts)
... >> it is necessary to distinguish finite from infinite. ... >ordinals start with 1, just as the ancients did, and only introduce ... >zero after the negatives have already been introduced. ... So cardinals are defined, in terms of sets of ordinals, like ...
(sci.math)
• Re: Mathematical concepts
... >concept of counting to pre-schoolers. ... How does one KNOW that finite cardinals make sense? ... For ordinals, even infinite ordinals, it is ... >> Counting on fingers is ordinal. ...
(sci.math)
• Re: Mathematical concepts
... >> Counting is ordinal, not cardinal. ... correspondence between the two for finite ordinals and ... cardinals, preserving the arithmetic operations, is ... Teachers need to be educated, ...
(sci.math)
• Re: Amateur continuum hypothesis question
... There are two common kinds of transfinite "number": ordinals and cardinals. ... The well-ordering theorem I stated above implies ... correspondence with an initial segement of Y. The basic property I ...
(sci.math)