## ihatealgebrasomuch Group Title what exactly is a 'real number' does that mean whole # or can it be like .5? one year ago one year ago

1. lstrasmann Group Title

yeah, i think real numbers can be basically any number on the number line (including decimals and fractions) according to wikipedia it includes integers fractions and unrational numbers (Pi for example)

2. estudier Group Title

whole # - this is not defined by mathematicians (use integer, positive integer, natural number, etc)

3. TuringTest Group Title

a real number is any number that appears on the real line; i.e. does not have an imaginary (complex) part complex numbers involve $i=\sqrt{-1}$which is not a real number, because there is no real number $$(-\infty,\infty)$$ number that satisfies $$\sqrt{-1}$$ our guesses might be 1 and -1, but...$1\cdot1=1\neq-1$and$(-1)(-1)=1\neq-1$so there is no "real" number that satisfies the expression real numbers in no way have to be whole numbers

4. ihatealgebrasomuch Group Title

so, .5 is a real number?

5. TuringTest Group Title

does it have any complex part in it ? an $$i$$ or $$\sqrt1$$ ?

6. TuringTest Group Title

I mean $$\sqrt{-1}$$

7. estudier Group Title

0.5 + 0i

8. TuringTest Group Title

oh you cheater :P

9. estudier Group Title

:-)

10. TuringTest Group Title

it must have a non-zero complex part to be exact

11. TuringTest Group Title

...if it is *not* to be a real number, that is

12. estudier Group Title

But isn't the real line part of the complex plane?

13. TuringTest Group Title

all real numbers are complex, not all complex are real if I am phrasing it poorly above I am only being too lazy since I'm about to leave, sorry :/

14. estudier Group Title

s'K, just kidding a bit, it's the algebraist in me......

15. TuringTest Group Title

good habit ;)

16. estudier Group Title

I bet OP wish she never asked now.....:-)

17. ihatealgebrasomuch Group Title

so is .5 a real number???

18. estudier Group Title

A simple answer is that pretty much all the numbers you are used to (including 0.5) are real.