On Mon, May 18, 2015 at 08:50:50PM +0200, Jos Koot wrote:
>
> At the mathematical level equality is a difficult and in many cases even an
> unsolvable thing.

Indeed.  It is suspected by some that difficulties with equality lie at 
the root of problems with set theory.

There are two concepts of equality:

(a) equality from below, which defined two sets to be equal iff they 
have the same elements, and

(b) equality from above, which defines two sets as being equal iff they 
have the same properties.

Set theory conflates these two concepts.

Scheme has various eqialities, but they are all equalities from below.

-- hendrik

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