Re: naive question from a non-mathematician


Hero wrote:
Stephen Montgomery-Smith schrieb:
David C. Ullrich wrote:
On Sun, 28 May 2006 18:12:02 GMT, Stephen Montgomery-Smith
<stephen@xxxxxxxxxxxxxxxxx> wrote:


G.E. Ivey wrote:

It's hard for me to believe this has gone on so long. While every "quibble" is correct (and mathematicians love quibbles!) John Smith did say "mathematically equivalent", not "identical" or "the same" or "equal" so I would have no trouble at all accepting "Yes, they are mathematically equivalent".

That's a great answer.

So it's up to generalisation:
Is there in the whole area of maths any structure with a
multiplication, where
0 * something is different from 0? And is there any structure with an
addition, where
something + 0 is different from something? [etc]

According to standard terminology, no. If you want to change the
definition of 0 and/or consider things other than rings, fields, etc.,
yes.

0 is defined, way back in Group Theory, to be the additive identity;
that is, 0 is the element x such that for all y,
x + y = y + x = y,
if such an x exists.

Since groups are considered part of rings, fields, ordered fields,
topological fields, etc., this additive property of 0 still remains
true, and you can prove things such as: In a ring,
0 * x = 0
for all elements x in that ring.

--- Christopher Heckman

.

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