# Talk:Transitive property of equality

When is a difference in an approximation *not* an error?
-- Toby 12:49 19 May 2003 (UTC)

- This is not only about approximations. Two cars may be approximately equal, without one being a little wrong. - Patrick 13:47 19 May 2003 (UTC)

In *x* ≈ *y*, no claim is (necessarily) being made that either *x* or *y* is an approximation.
But the approximate equation *itself* is an approximation -- it is there that the error lies.
That is, in the context of approximations, what "error" means -- the difference between quantities that are labelled "approximately equal".
Of course, error doesn't necessarily mean "mistake" here.
However, that is a somewhat technical use of the word, so let me just remove it altogether -- we don't need it when "difference" will do.
-- Toby 14:55 19 May 2003 (UTC)

- Okay, in this technical sense "error" is the same as difference, but without the explanation the latter is clearer. Patrick 15:26 19 May 2003 (UTC)

I know its not standard mathematical practice, but I like the notion of using

For every variable "x", "y", and "z" - its more clear to some people and I think its more correct as well; for example, I might say, I met a guy, lets call him "Johnny" Pizza Puzzle

It's not more correct unless you say "Let's call them [...]". -- Toby Bartels 05:25 12 Jun 2003 (UTC)

## Problem with the linguistic example[edit]

The problem with the specific example in the article is that the relationship between men and talking is different than between talking and stupid, and hence the transitive property doesn't hold. The relationship between men and talking is "do", or in more mathematical terms do(men, talking). The do relationship isn't even an equivalence relation, because do(men, talking) doesn't imply do(talking,men). The relationship between talking and stupid is "is", or is(talking, stupid), which also isn't an equivalence relationship, because is(talking,stupid) doesn't imply is(stupid,talking).

In order to reach the conclusion that men are stupid you would have to have a relationship such as:

For all X where do(X,talking) then is(X,stupid)

or in plain English

Anyone who talks is stupid.

The problem is that it isn't an equivalence relation. Joshuajohanson (talk) 17:00, 6 February 2009 (UTC)