True == 1 weirdness

[Ian Kelly]

On Fri, Sep 18, 2015 at 1:12 PM, Random832 <random832 at fastmail.com> wrote:
> On Fri, Sep 18, 2015, at 14:24, Terry Reedy wrote:
>> The semantics Python copies from math is "a op b op c == a op b and b op
>> c",
>
> I don't believe those *are* the semantics in math. I believe that in
> math this notation is *specifically* meant to support "all of these
> things are related to all of the others in ways that can be summarized
> in a single expression" and that mixing operations in a way that does
> not allow that is a misuse of the notation. In other words, any "a op b
> op c" that does not allow you to make a statement on how a is related to
> c is a *mistake*, because it means that you're welding together two
> things that aren't logically connected to each other at all.
>
> If there is no operator op3 where a op1 b op2 c implies a op3 c, then
> you should not put a and c in the same inequality, full stop.

Whoever wrote the Wikipedia article disagrees:

https://en.wikipedia.org/wiki/Inequality_(mathematics)#Chained_notation

Although the reference to Python leads one to suspect that this could
be based more on Python's semantics than on actual mathematics.