Re: Basic set theory question
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Sun, 28 Jan 2007 10:04:44 -0600
On 28 Jan 2007 11:44:23 +1100, Logan Lee <10464307@xxxxxxxxxx> wrote:
David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx> writes:
On 27 Jan 2007 15:23:42 +1100, Logan Lee <10464307@xxxxxxxxxx> wrote:OK. Please teach me why they are not contradictory.
Dave Seaman <dseaman@xxxxxxxxxxxx> writes:
On 27 Jan 2007 11:47:24 +1100, Logan Lee wrote:Quote: 'The choice to _use_ TeX was yours, not mine'
Dave Seaman <dseaman@xxxxxxxxxxxx> writes:
On 26 Jan 2007 16:41:09 +1100, Logan Lee wrote:If you gonna use TeX to express math symbols as in \subseteq why don't you also use \forall instead of 'A' which is confusing?
Logan Lee <10464307@xxxxxxxxxx> writes:
What is the difference between
A \in B
A is an element of B.
and
A \subseteq B?
A is a subset of B.
--
### Author "Logan Lee" ###
### HomePage http://beam.to/pyenos ###
Also, what are the formal definitions of
A \in B
and
A \subseteq B?
The former does not have a definition; it is an undefined primitive.
The latter is defined by
A \subseteq B <-> Ax((x \in A) -> (x \in B)).
Like this:
A \subseteq B \Leftrightarrow \forall x ((x \in A) \Rightarrow (x \in B))
In this way, regardless of readability issue, one could translate it to symbols simply by following rules and copying down on to paper in symbols.
The choice to use TeX was yours, not mine. I used it in the case of
\subseteq only because you specifically asked about the meaning of that
symbol.
=> 'I didn't choose to _use_ TeX' => 'I didn't _use_ TeX'
Um, that last implication is ridiculous. You didn't choose
to be born on your birthday. Hence you were not born on
your birthday?
Quote: 'I _used_ it...'
=> 'I didn't choose to _use_ TeX but I _used_ it' => 'I didn't _use_ TeX but I _used_ it'
You seem to be contradicting yourself ;)
Only to someone with severely limited understanding of logic.
I did. Please read what I wrote.
************************
David C. Ullrich
.
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