Are imaginary numbers real?

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Re: Are imaginary numbers real?
« Reply #30 on: September 27, 2016, 11:57:28 PM »
Does a number have to be constructed to garner any validity?
Formally, yes. You can't take a number from your pocket and claim it has real number properties.

If you don't care about constructions, it's not a problem. You can simply set axioms that uniqely define real numbers and viola, you have them without any rocket science preparation.

Does pi have to be constructed in some fashion; isn't its definition enough for its existence?
The definition only tells you how to find that number in uniqe way. It doesn't need to mean the number itself
is constructed (that is: as  a segment (geometry - impossible) or a number (calculus - possible with series)). This is common: you know that something exists, but you don't really know how it looks as entirety.

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.
Yes, only "ruler and compass". I don't really understand the rest of your post.

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UpstartPixel

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Re: Are imaginary numbers real?
« Reply #31 on: September 28, 2016, 04:10:40 AM »
Yes, only "ruler and compass". I don't really understand the rest of your post.

I just meant that since you said we can "only process rationals", showing how to construct a real number geometrically would refute that. But OK, we're wandering a bit into the weeds here. Ignore me :)

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mathsman

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Re: Are imaginary numbers real?
« Reply #32 on: September 28, 2016, 11:29:27 AM »
In reality, real numbers don't exist. All numbers we can process are rational.
I may be misunderstanding you. Are you suggesting that the rational numbers have an existence we cannot extend to the rest of the reals?

Re: Are imaginary numbers real?
« Reply #33 on: September 28, 2016, 11:16:55 PM »
What I mean is that we are unable to process the entire real number. Take pi for instance - you don't know all decimals. You can only operate on rational approximations. Take sqrt(2). It exists only as an abstract number, but you can't provide its decimal representation. It's like computers - they only operate on finite number of bits, therefore all numbers are rational for them.

On the other hand, rationals can be a base to define all real numbers (for instance equivalence classes of Cuachy sequences), so in that sense the extension is a proper word.

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UpstartPixel

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Re: Are imaginary numbers real?
« Reply #34 on: September 28, 2016, 11:50:13 PM »
Aha, so by process you mean "define via an algorithm of a Turing machine"?

In that sense there is reason to doubt that reals are real.

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mathsman

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Re: Are imaginary numbers real?
« Reply #35 on: September 29, 2016, 10:28:13 AM »
What I mean is that we are unable to process the entire real number. Take pi for instance - you don't know all decimals. You can only operate on rational approximations. Take sqrt(2). It exists only as an abstract number, but you can't provide its decimal representation. It's like computers - they only operate on finite number of bits, therefore all numbers are rational for them.

On the other hand, rationals can be a base to define all real numbers (for instance equivalence classes of Cuachy sequences), so in that sense the extension is a proper word.

Can't we say the same about 1/3? 1/3 can't be expressed exactly as a decimal.


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Re: Are imaginary numbers real?
« Reply #37 on: September 29, 2016, 11:33:15 AM »
Pi isn't even a rational number...
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Re: Are imaginary numbers real?
« Reply #38 on: September 29, 2016, 11:45:42 PM »
Can't we say the same about 1/3? 1/3 can't be expressed exactly as a decimal.
But can as a finite number of elementary operations on numbes.  Besides, we know all decimals.

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Re: Are imaginary numbers real?
« Reply #39 on: September 30, 2016, 03:51:23 AM »
sandokhan, read the first two lines of your thread.
Quote
The irrationality of the square root of 2 HAS NOT BEEN PROVEN, this is the point I am trying to make.
This is miserably wrong. I can prove it to you myself if you desire.

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Re: Are imaginary numbers real?
« Reply #40 on: September 30, 2016, 04:15:35 AM »
sandokhan, read the first two lines of your thread.
Quote
The irrationality of the square root of 2 HAS NOT BEEN PROVEN, this is the point I am trying to make.
This is miserably wrong. I can prove it to you myself if you desire.

I'm interested  :)

Edit: Lol nevermind 10sec google and I got it.
« Last Edit: September 30, 2016, 04:18:17 AM by User324 »
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wise

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Re: Are imaginary numbers real?
« Reply #41 on: September 30, 2016, 04:32:39 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.

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. :)

You're wrong.

mass should be negative if we are talking about antimatter. research about "what is antimatter". This is theorically possible. You can say about it phsically or mathemetically possible, anyhow it is possible. If you write Einstein's law E = mc^2, there is two answers for mass. One of positive and the other one is negative. You can find out a knowledge about this matter by searching about Paul Dirac.

His research marked the first time something never before seen in nature was “predicted” – that is, postulated to exist based on theoretical rather than experimental evidence. His discovery was guided by the human imagination, and arcane mathematics.

For his achievement Dirac was awarded the Nobel prize for physics in 1933 at the age of 31.

I saw some news about some experiments antimatter found on CERN, but i don't know are they published the results or not. If it is phsically impossible, why are scientists working on it?
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Re: Are imaginary numbers real?
« Reply #42 on: September 30, 2016, 06:54:14 AM »
mass should be negative if we are talking about antimatter.
Quote
The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.
Taken from wikipedia.

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wise

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Re: Are imaginary numbers real?
« Reply #43 on: September 30, 2016, 06:56:57 AM »
mass should be negative if we are talking about antimatter.
Quote
The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.
Taken from wikipedia.

Which one is got Nobel phsics award is Paul Dirac is a special one shown the mass can be negative or wikipedia which can writen by everybody shows mass isn't.
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Re: Are imaginary numbers real?
« Reply #44 on: September 30, 2016, 08:08:15 AM »
Wikipedia isn't the best source of information. You should either quote academic or find a proper article descibing the topic.

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mathsman

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Re: Are imaginary numbers real?
« Reply #45 on: September 30, 2016, 12:05:47 PM »
Can't we say the same about 1/3? 1/3 can't be expressed exactly as a decimal.
But can as a finite number of elementary operations on numbes.  Besides, we know all decimals.

You'll have to help me here. The square root of 2 can be calculated by hand using very simple arithmetic to any accuracy you desire. In what way does this differ from the calculation of 1/3 by, for example, long division?

I'm not sure what you mean by 'Besides, we know all decimals.'

Re: Are imaginary numbers real?
« Reply #46 on: September 30, 2016, 06:37:35 PM »
You'll have to help me here.
The choice of a base10 numbering system is arbitrary.   

Re: Are imaginary numbers real?
« Reply #47 on: September 30, 2016, 11:33:33 PM »
You'll have to help me here. The square root of 2 can be calculated by hand using very simple arithmetic to any accuracy you desire. In what way does this differ from the calculation of 1/3 by, for example, long division?
The difference is that one number can be presented as an abstract division of two integers, whereas the other can't. Also, knowing one of them is a fraction allows presenting that number in other (integer-based) positioning system where the amount of decimals is finite. 1/3=0.1 in ternary.  For irrational numbers one can't find such base.

I'm not sure what you mean by 'Besides, we know all decimals.'
We know that 3 repeats endlessly. There's no rule of periodicity for sqrt(2).

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UpstartPixel

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Re: Are imaginary numbers real?
« Reply #48 on: October 01, 2016, 11:03:00 AM »
mass should be negative if we are talking about antimatter.
Quote
The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.
Taken from wikipedia.

Which one is got Nobel phsics award is Paul Dirac is a special one shown the mass can be negative or wikipedia which can writen by everybody shows mass isn't.

Sigh...once again you are just making stuff up. Antimatter is about charge, not about mass. A positron is an electron with positive charge, not negative mass. Read the speech to Dirac's Nobel prize here:
http://www.nobelprize.org/nobel_prizes/physics/laureates/1933/press.html

"It now appeared that one of the solution systems required the existence of positive electrons having the same mass and charge as the known negative electrons."

You really need to learn about basic quantum theory. What kind of an engineer are you anyway?

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Re: Are imaginary numbers real?
« Reply #49 on: October 01, 2016, 12:50:51 PM »
mass should be negative if we are talking about antimatter.
Quote
The overwhelming consensus among physicists is that antimatter has positive mass and should be affected by gravity just like normal matter.
Taken from wikipedia.

Which one is got Nobel phsics award is Paul Dirac is a special one shown the mass can be negative or wikipedia which can writen by everybody shows mass isn't.

Sigh...once again you are just making stuff up. Antimatter is about charge, not about mass. A positron is an electron with positive charge, not negative mass. Read the speech to Dirac's Nobel prize here:
http://www.nobelprize.org/nobel_prizes/physics/laureates/1933/press.html

"It now appeared that one of the solution systems required the existence of positive electrons having the same mass and charge as the known negative electrons."

You really need to learn about basic quantum theory. What kind of an engineer are you anyway?
Oh no, stop confronting him with reality. You'll break his world apart :(
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Re: Are imaginary numbers real?
« Reply #50 on: October 03, 2016, 07:47:01 AM »
Mass is scalar. It canntnge negative.
I wonder how obnoxious I can make my signature?
Please give me ideas.

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Master_Evar

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Re: Are imaginary numbers real?
« Reply #51 on: October 03, 2016, 12:03:27 PM »
If mass was negative, then it's momentum would also be negative. In which case, if a piece of matter and negative matter collided (and they don't annihilate each other), they would push each other so that they both accelerated in one direction. This would result in a source of infinite energy.
Math is the language of the universe.

The inability to explain something is not proof of something else.

We don't speak for reality - we only observe it. An observation can have any cause, but it is still no more than just an observation.

When in doubt; sources!

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UpstartPixel

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Re: Are imaginary numbers real?
« Reply #52 on: October 05, 2016, 09:37:09 AM »

Oh no, stop confronting him with reality. You'll break his world apart :(

I can abide weird debate, but I draw the line at assertions or quotes that are so obviously wrong.
Also, it depends whether I woke up with a hangover, among other things :)

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UpstartPixel

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Re: Are imaginary numbers real?
« Reply #53 on: October 05, 2016, 09:51:06 AM »
Oh no, stop confronting him with reality. You'll break his world apart :(

Heh, must have already happened, because I think I'm on his ignore list now. Do I get a medal or a candy bar or something?

Seriously, posers like Intikam irritate me. I have to believe that this site was built because some folks want to honestly develop the flat earth point of view. But when amateurs like Intikam suck up the air calling themselves flat earth scientists while not knowing basic math and physics, it puts that effort in a more than embarrassing light.

And besides, it's not even fun to debate rank stupidity :)

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Re: Are imaginary numbers real?
« Reply #54 on: October 05, 2016, 02:30:13 PM »
What I mean is that we are unable to process the entire real number. Take pi for instance - you don't know all decimals. You can only operate on rational approximations. Take sqrt(2). It exists only as an abstract number, but you can't provide its decimal representation. It's like computers - they only operate on finite number of bits, therefore all numbers are rational for them.

On the other hand, rationals can be a base to define all real numbers (for instance equivalence classes of Cuachy sequences), so in that sense the extension is a proper word.

Can't we say the same about 1/3? 1/3 can't be expressed exactly as a decimal.

You can express it exactly in a non-decibel system.  Pi can even be expressed precisely.