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imaginary

Defines: 
imaginary, imaginary number, imaginary element, purely imaginary number, purely imaginary, pure imaginary number, pure imaginary
Synonym: 
pure complex
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

12D99 no label found

Comments

The real part of 0 is 0; consequently, 0 is an imaginary number (?)

I'd say yes then
so? ;)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

by the way, 0 is ALSO a complex number ;)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

To drini
Naturally, 0 and 50 are complex numbers, but 50 is not imaginary. Do you mean that 0 is imaginary??
Jussi

In Finland, and I think also in continental Europe, the term "imaginary" means a complex number having the imaginary part distinct from zero. We have also the term "purely imaginary" which means that the real part is zero (so, e. g. 3i and 0 are purely imaginary -- although 0 is real, too) =o)
Jussi

Yes, I meant 0 is both imaginary and real
(just like it's als integer, complex, rational, etc).

The purely imaginary vs imaginary I don't think it's standard (it's more matter of style for agiven prof or inside a school), but if you asked me , I would have guessed imaingary is real part = 0 (thus 0 is imaginary) and purely imaginary the complex part different from zero (so 0 wouldn't be purely imaginary)

I guess conventions vary in differents parts of the world.

But yes, I meant 0 is imaginary

f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

So, the terminology is different in different parts of the world -- I have known it also before. But, in my opinion, the "Finnish terminology" is somewhat clearer, and I guess that in the history, when the _imaginary_ numbers were introduced (who did it?), nobody thought that the well-known zero were imaginary!
Jussi

hehehe,, well
when imaginary numbers wre introduced around 16 or 17 century, someitmes even negative numbers would not be considered numbers...

but by the time imaginary numbers were acknowledged as an algebraic structure C (call it field or whatever), 0 would already be considered an imaginary number (methinks) albeit a rather special one (kinda like empty set isa very special set, or 0! or some such particularities)

f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

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