Are negative numbers any less real than positive numbers?

Question

skullpatrol · Answer

My definition of a real number is any number that is either positive, negative, or zero.

skullpatrol · Answer

These numbers can be paired with the points on a number line, thereby showing their order. Note: if when you draw a number line you have TWO oppositely pointing arrow-heads, <---------------------> then you MUST have an origin marked as "0" and positive and negative numbers on either side. <----------0---------->

zzr0ck3r · Answer

In a pure mathematical description they are just inverses of their positive counter part. i.e. $-a$ is just the thing we need to combine with our operation addition to get our additive identity.

zzr0ck3r · Answer

negative is really a bad name for them:) We could have just as easily said $a+\overset{\&}{a}=0$

skullpatrol · Answer

With the important note:

0 is neither positive nor negative 

That is, 0 has no sign.

zzr0ck3r · Answer

right, it is its own inverse and has order 1

zzr0ck3r · Answer

Positive integers came first, and then we found 0. then we needed to be able to get to 0 from our positive numbers. :)

alekos · Answer

That's right, and it took a long time to get to the zero concept

mww · Answer

real numbers are crazy things. Burn them with fire!

Non-real numbers are much more fun but they still rely on real numbers.

skullpatrol · Answer

https://m.youtube.com/watch?v=SvFfVtRT1UI

thomas5267 · Answer

Are numbers real?

skullpatrol · Answer

We use them in real life :-)

thomas5267 · Answer

But does that make it real?  Where can I find the number 1 in the real world?

skullpatrol · Answer

The number one represents a particular number. 

It is the name for its value.

thomas5267 · Answer

Find me that number in the real world lol.

thomas5267 · Answer

In case no one gets it, what I am trying to say is numbers are not real in the sense that an apple is real.  It is very easy to show that apple is real by handing you an apple but I certainly couldn't hand you a number to show that it is real (whatever handing you a number means).

kainui · Answer

Let's say you have an empty room and then someone walks out of it. Does that mean someone has to walk back into the room in order for it to be empty again?

thomas5267 · Answer

What?  How can an empty room have someone walk out of it?

zzr0ck3r · Answer

one is an idea, it is the idea that if I want to take two things and make it another thing, then one is the thing we do to something to not change that thing. 

numbers can be represented by real things and vice versa