Are imaginary numbers real?

Yes, they are. Right?

No thei aren't.

By definition, they are not.

i begs to differ, but you can't argue with a dictionary.

No thei aren't.

Mai be mi imagination, but, did you spell thei wrong?

i is the symbol for an imaginary number such that i²=-1.

i is the symbol for an imaginary number such that i²=-1.

Exactly. I can use it in equations and get real results!

Iowa's answering Bullwinkle's question.

i is the symbol for an imaginary number such that i²=-1.

Just for the record, the above isn't a definition of i.

That's what I learned it was.

What is the formal definition?

According to Wikipedia, they have been with us since Heron of Alexandria. No one has disproven them, so they are indeed real.

If that were the definition, then we run into troubles, because (-i)^2=-1 as well...

When you introduce complex numbers, you can define them as a pair of real numbers (a,b) with actions:
(a,b)+(c,d)=(a+c,b+d),
(a,b)*(c,d)=(ac-db,ad+bc).

Then i is defined as a pair (0,1) and from the * definition it follows that (0,1)*(0,1)=(-1,0).
Now if you think of a pair (a,b) as a+ib (that notation requires some care, but only from formal point of view), then i^2=-1.

So i^2=-1 is not a definition, it's a property.

About the OP. There's an old joke.
i and pi talks.
pi: get real.
i: get rational.

Actually, i^2=-1 is part of the definition of i.

Although at university we've been told that the definition of i is i^2 = -1

About the OP. There's an old joke.
i and pi talks.
pi: get real.
i: get rational.

Heh, good one

I think an equivalent quesion would be: Are real numbers real?

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

I think an equivalent quesion would be: Are real numbers real?

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

Bullshit.

I think an equivalent quesion would be: Are real numbers real?

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

Heh, nice counter. You're actually right. There's a whole school that disputes that 0.99999...= 1.
But then that would practically make the imaginaries more real than the reals.
That's what I'm talking about 

Are imaginary numbers real?

All numbers are imaginary.  Numbers are a man-made construct. 

COROLLARY:  Every thing is connected to every thing else. 

BRUTAL TRUTH:  There is no empty vacuum space. 

Quote from: UpstartPixel on September 23, 2016, 10:32:30 AM

Are imaginary numbers real?

All numbers are imaginary.  Numbers are a man-made construct. 

COROLLARY:  Every thing is connected to every thing else. 

BRUTAL TRUTH:  There is no empty vacuum space.

You have no idea what this thread is about, do you?

You have no idea what this thread is about, do you?

I know more than that!! 

I know how many devils are dancing on your fictitious "globe" model!!! 

Quote from: UpstartPixel on September 25, 2016, 07:03:52 AM

You have no idea what this thread is about, do you?

I know more than that!! 

I know how many devils are dancing on your fictitious "globe" model!!!

Your profile Pic is upside down-->he is on the bottom of the globe. Globe earth = 100% proven.

Real life: Not in real life on this universe but It is possible on opposite universe.

Theory: if energy is negative but mass is positive, c^2 = (-)  so speed is imaginary. Or oppositely if there is an antimatter but energy is normal, then c^2= (-) again.

Theorically possible.

Real life: Not in real life on this universe but It is possible on opposite universe.

Theory: if energy is negative but mass is positive, c^2 = (-)  so speed is imaginary. Or oppositely if there is an antimatter but energy is normal, then c^2= (-) again.

Theorically possible.

His signature

ignore list: rabinoz, sokarul
Alive*, Ba*H*, Cir*, cru*, dis*, Ome*, Tot*, U*324, zo*, bul*, boyd*

So this guy is basically talking to himself.

Quote from: İntikam on September 26, 2016, 01:47:00 AM

Real life: Not in real life on this universe but It is possible on opposite universe.

Theory: if energy is negative but mass is positive, c^2 = (-)  so speed is imaginary. Or oppositely if there is an antimatter but energy is normal, then c^2= (-) again.

Theorically possible.

His signature

Quote

ignore list: rabinoz, sokarul
Alive*, Ba*H*, Cir*, cru*, dis*, Ome*, Tot*, U*324, zo*, bul*, boyd*

So this guy is basically talking to himself.

Nah, he's still talking to me
For now.

Real life: Not in real life on this universe but It is possible on opposite universe.

Theory: if energy is negative but mass is positive, c^2 = (-)  so speed is imaginary. Or oppositely if there is an antimatter but energy is normal, then c^2= (-) again.

Theorically possible.

No, *mathematically* possible. You have to learn the difference between what is mathematically allowed and what is physically possible.

Einstein's E = mc^2 gives an equivalence between mass at rest and its equivalent energy. You can't just put a negative sign on one side and then - because mass is always positive - conclude that Whee!! the speed of light must be imaginary. For your information the equivalent energy in that equation is always positive.

So you are just playing with mathematical symbols, but that doesn't mean there is any physics behind what you are doing. Sorry, not impressed.

I think an equivalent quesion would be: Are real numbers real?

In reality, real numbers don't exist. All numbers we can process are rational.

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

Real numbers are far more difficult to define/construct (although it depends on the approach) than complex (imaginary) numbers.

I think an equivalent quesion would be: Are real numbers real?

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

Where do rational number appear in nature? I've never seen one.
You do know that rational numbers are also real numbers don't you?

Quote from: Kami on September 24, 2016, 08:25:41 AM

I think an equivalent quesion would be: Are real numbers real?

In reality, real numbers don't exist. All numbers we can process are rational.

Quote from: Kami on September 24, 2016, 08:25:41 AM

In my opinion we can not argue about rational numbers, as they indeed appear in nature. Real numbers, on the other hand, are as much a theoretical construct as imaginary numbers.

Real numbers are far more difficult to define/construct (although it depends on the approach) than complex (imaginary) numbers.

Not if you go the geometric route, it would seem to me. I can easily draw a square of side = 1, and then draw its diagonal.

Not if you go the geometric route, it would seem to me. I can easily draw a square of side = 1, and then draw its diagonal.

Not all real numbers can be constructed that way.

Does a number have to be constructed to garner any validity?
Does pi have to be constructed in some fashion; isn't its definition enough for its existence?

Quote from: UpstartPixel on September 27, 2016, 03:37:21 AM

Not if you go the geometric route, it would seem to me. I can easily draw a square of side = 1, and then draw its diagonal.

Not all real numbers can be constructed that way.

By "that way" I assume you mean the classic "ruler and compass" construction, and that is true. But I meant to challenge your assertion that we can only process rationals by suggesting how to construct one.