Question

is an imaginary number a real number always sometimes or never true?

Answer 1

is an apple a orange always, sometimes, or never true ? :)

Answer 2

are you not familiar with phrase ... " trying to compare apples with oranges"

Answer 3

yeah I understand it now

Answer 4

my point is that they are opposites so by definition they cannot be same thing

Answer 5

hmm 0i is a bit annoying imaginary number

Answer 6

im not so sure, but the real and imaginary numbers seem to meet at 0

Answer 7

real numbers are complex numbers with an imaginary part equal to zero
so are complex numbers real?

Answer 8

but the question is about sometimes/always/never right ?

Answer 9

by definition, it seems 0 falls in both imaginary and real numbers so im inclining more towards `sometimes`

Answer 10

yeah, and from the venn diagram it should be clear which of those fits

Answer 11

look, based on the diagram I drew, is 1 a complex number?

Answer 12

yes but how is that related to the original question ?

Answer 13

well if by "imaginary number" they mean "complex number", then 1 is an example of an imaginary number that is part of the set of real numbers

Answer 14

though i'm not positive they mean that imaginary=complex, the terminology seems a bit vague

Answer 15

hm that's not my understanding...

Answer 16

imaginary numbers are the ones without a real part

Answer 17

like : 0 + bi

Answer 18

Ah, my understanding of terminology has failed me again :P
You are right, ganshie

Answer 19

im just quickly going thru wolfram haha!

Answer 20

http://mathworld.wolfram.com/PurelyImaginaryNumber.html

Answer 21

your source is better than mine:
http://www.mathsisfun.com/sets/number-types.html

Answer 22

@TuringTest your terminology looks more standard. Also wolfram agrees with it as the question stands..
http://mathworld.wolfram.com/ImaginaryNumber.html

Answer 23

\[\mathbb{R}=\left\{ a+bi| b \neq 0 \right\} \\ \text{ So } 0 \in R \\ \text{ Imaginary }=\left\{ a+bi |a =0 \right\}\\ \text{ But I don't I have seen anybody defined the imaginary numbers with } b \neq 0 \\ \text{ So }0i=0 \in \text{Imaginary }\]

Answer 24

So I think I agree with @ganeshie8 as well

Answer 25

lets not over complicate this guys
i assume imaginary is not same as complex

i admit i didn't consider 0 as being imaginary :{

Answer 26

oops I made an error up there b=0

Answer 27

Descartes added some confusions to terminology it seems

Answer 28

lol but the wolfram link does seem to cast some doubt on the meaning of imaginary number. at this point I am inclined to go with the simple interpretation as well and go with ganeshie's first answet

Answer 29

answer
why can i not see the "post" button when i write more than 3 lines? anyone else seeing this?

Answer 30

http://mathforum.org/library/drmath/view/65170.html
This one guy also says 0 is an imaginary number

Answer 31

Clearly the author of this question thought the matter was more simple than it is.

Answer 32

Well I don't think I would have thought of the 0i thing without @ganeshie8 bringing that up.

Answer 33

So I probably would have thought the question was more simple then.

Answer 34

if we assume imaginary to be complex, then the answer is "sometimes"
if we assume 0 is imaginary, the answer is "sometimes"
if we define imaginary as having a non-zero imaginary part and zero real, it is "never"

Answer 35

I think we need to know how Emily's math teacher defined the real numbers and imaginary numbers in class.

Answer 36

^agreed