Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Starver]

Numbers are called "imaginary" when b is not = 0

...but a is zero.

If a is non-zero, then it's either real (zero imaginary component) or complex (a mixture).

If both a and b are zero, it can belong to real, imaginary or complex realms, of course.

Anyway "5" is a fully Real number, or a Complex number that just happens to have a zero Imaginary component.  But it isn't Imaginary.

Anyhow, back to where this all came from, velocities greater than c create Imaginary factors in the whole time/length/weight alteration equations.  Which aren't the same as negative factors.

[Reelya]

Imaginary number CAN have "a NOT zero". "5 + 3i" is an imaginary number. It's nonsense to say a must equal zero for an imaginary number.

I wrote :-

Numbers are called "imaginary" when b is not = 0

It doesn't make a difference what "a" is, "a" is assumed to be a scalar factor, however.


You wrote:

"Anyway "5" is a fully Real number, or a Complex number that just happens to have a zero Imaginary component.  But it isn't Imaginary."

^ isn't this exactly what i said, a=5, b=0 hence not imaginary. So how does that conflict with what i wrote, which was :-

That's because you can conceive of 5 apples, even -5 apples (a debt in apples), or 1.5 apples (1 and half apples).

You cannot conceive of an amount of apples "five times square root of negative 1".

Where i'm clearly making a distinction between "5" as a conceivable amount (real) and "5i" as a non-conceivable amount (imaginary).

[Osmosis Jones]

Imaginary number CAN have "a NOT zero". "5 + 3i" is an imaginary number. It's nonsense to say a must equal zero for an imaginary number.

Formal definition disagrees with you I'm afraid.

From wiki;

An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1.[1] The square of an imaginary number is less than or equal to zero. For example, 5i is an imaginary number and its square is −25. According to some definitions, zero (0i) is not regarded as an imaginary number, but as a pure real.

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where a and b are called, respectively, the real part and the imaginary part of the complex number. Imaginary numbers can therefore be thought of as complex numbers whose real part is zero.

[Starver]

Reelya: Wiki definition has already been given, but "Numbers are called "imaginary" when b is not = 0" is just the wrong thing to say.  Or not right in the right way.  Because Imaginary numbers include 0i, where b=0 and don't include any cases where a!=0.

You wrote:

"Anyway "5" is a fully Real number, or a Complex number that just happens to have a zero Imaginary component.  But it isn't Imaginary."

^ isn't this exactly what i said, a=5, b=0 hence not imaginary.

Actually, you said imaginary was b!=0. (Not right, as explained above.)  And nothing about what was not imaginary.  Or appear to have said it later.

I think, looking at it, that you perhaps had intended to say "a=0" but accidentally wrote "b=0" then corrected yourself by switching to "b!=0", by accident.  Easily done, and I'm quite possibly making a similar typo error in this very post.

(Cookies are available if you spot what errors I might have allowed to happen.)

[Reelya]

5 is a real number whichever way you look at it, i certainly never said 5 was imaginary, nor would it be by what i wrote.

Though, i should have said "complex" not imaginary. I always though of xi as the "imaginary component". i guess i conflated the terminology of imaginary with the broader concept of complex. It's been quite a while since i formally studied this stuff and needed to use specific terminology.

I did mean to say b != 0, but that's describing complex vs real, i guess. So when i said "imaginary" i meant what you mean by "complex". I'll be more careful in future.

[Starver]

Certainly some apologies, I got twisted up as to who said what originally...

'Twas:

Well, 5 (and any other real number) is also imaginary number.

With my reply of "No, But it is complex, [..] Is that what you're thinking of?" that came first.

But then you also responded to Kogut with the (wrong and/or badly written) assertion that Imaginary numbers had b!=0[1], which I then responded to.  And then things may have gotten complicated.

The following table should apply, typos excepted.

	a==0	a!=0
b==0	Zero (I, R & C)	Real (R & C)	<- All and only these are Real numbers on this row
b!=0	Imaginary (I & C)	Complex (C)
	^All/only these are Imaginary on this column		All rows and columns are within the set of Complex numbers

(Sorry, couldn't find a way of putting the "Double-line" characters in for I, R and C, that I find most commonly used.)




[1] By the time I was reading it.  From Putnam's message I gather you'd had it as plain b=0, originally...

[Reelya]

Because you get a negative square root in the relativity equations once you go past light speed. Hence imaginary time. Clarifying the semantics of this has been the topic for the last page or two.