## ihatealgebrasomuch 3 years ago what exactly is a 'real number' does that mean whole # or can it be like .5?

1. lstrasmann

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

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

3. TuringTest

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

so, .5 is a real number?

5. TuringTest

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

6. TuringTest

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

7. estudier

0.5 + 0i

8. TuringTest

oh you cheater :P

9. estudier

:-)

10. TuringTest

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

11. TuringTest

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

12. estudier

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

13. TuringTest

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

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

15. TuringTest

good habit ;)

16. estudier

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

17. ihatealgebrasomuch

so is .5 a real number???

18. estudier

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