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? After all, 0 is considered
as { } or the empty set and as the neutral element of addition.
Friendly greetings
Hero

Or to rephrase your question - is zero a kind of "universal currency" amongst the whole of mathematics. For example:
0 the real number,
0 the complex number,
0 the 2D vector,
0 the 3D vector,
zero apples,
zero bananas,
$0.00,
are these all the same thing?
.