I sometimes wish I was doing computer science as it would be easier
Post me your hardest maths question you know
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I sometimes wish I was doing computer science as it would be easier
You say 'real'?
What about the difference between sqrt(-1) and sqrt(-9)
The difference is 2i. Which is an imaginary number
So are root -1 and root -9 the same?
I'm not arguing with you, I'm just genuinely intrigued
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Take two numbers, a and b, that are not identical. Now, a-b is not zero so they must be different. As they are different, then there must be a value (take (a+b)/2 as it's the obvious choice) that sits between a and b.
Two numbers being different implies an intermediate value. By the contrapositive, no intermediate value implies that the two numbers are the same.
You say real?
What about the difference between sqrt(-1) and sqrt(-9)
The difference is 2i. Which is an imaginary number
So are root -1 and root -9 the same?
I'm not arguing with you, I'm just genuinely intrigued
Pffft, my assertion assumed the context of the real numbers only. I probably should have mentioned that
Replace the word 'real' with the word 'complex' and you've got it (I think)...
You say real?
What about the difference between sqrt(-1) and sqrt(-9)
The difference is 2i. Which is an imaginary number
So are root -1 and root -9 the same?
I'm not arguing with you, I'm just genuinely intrigued
2i is not equal to 0, so they are not the same.
I know they are not, but his statement was.
Soldato
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No it's not, because the integers (whole numbers) form a countable set, whereas the real numbers are uncountable.
Please just accept that you're wrong
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Pffft, my assertion assumed the context of the real numbers only. I probably should have mentioned that
Replace the word 'real' with the word 'complex' and you've got it (I think)...
So should it be:
P.S. the inability to find a real number (or real coefficient of an imaginary) between two numbers is the definition of those two numbers being the same.
Recurring doesn't mean that 2 things are the same? Where did you get that from.
1/3 of 10 is not 3.3r. That is a fact is it not. Its as close as we can get to 1/3 of 10 but it is not 1/3 of 10 precisely. If you did 3 * 3.3r you will never get your 10 back.
Every time you repeat the recurring 9, you get a little bit closer to the 1, and the size of the next step you take is proportional to the remaining distance to 1. Thus you will never ever truly reach 1. Infinity represents something with no end point which means that you will never get to the point where you are equal to 1. You will always be out by a bit.
To provide something that might help get my point across. You can have 2 balls that are considered identical down to the atomic level. We would call them identical but if you had the ability to look deeper you would find differences. If you take the idea the two numbers are identical if there is not number between the two then 0.9r is equal to 1 but that not what I am arguing. I am saying that 0.9r will never be 1 by its very nature.
If your idea of 2 numbers being the same is that there is not a number that can sit between the two then fine.
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Soldato
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"Given two real numbers a and b, a = b iff there exists no real number c in (a, b)."
Take a complex number, which is a combination of a real and an imaginary, a+bi. Take another, c+di.
Now a+bi = c+di if a=c and b=d.
Seriously, you don't understand what 'recurring' means. It is defined so that 1/3 === 0.3r.
Calling it an approximation means you don't understand the meanings of the terms that you're using.
As I said before, smarter people than you or I overwhelmingly disagree with you.
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fez you are beyond it... enough genuine proofs have been displayed in this thread to convince a worm that 0.9r = 1.
Maths is one of the few things in which you can have a definite right and a definite wrong. And i hate to break it to you but you are wrong. Instead of banging your head against your wall of intuition, put your energy into trying to see why 0.9r does in fact equal one.
Maths is one of the few things in which you can have a definite right and a definite wrong. And i hate to break it to you but you are wrong. Instead of banging your head against your wall of intuition, put your energy into trying to see why 0.9r does in fact equal one.
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Well, if you dispute this, then you can throw the whole of modern mathematics out the window.
If you are working under the assumption that 0.3r = 1/3 of 1 then yes, 0.3r = 1/3 of 1.
I was under the impression that recurring represented the fact that there are an infinite number of the recurring value.
So 0.3r was the same as 0.33333.... with an infinite number of 3s. If that is the case then 0.3r * 3 will never exactly equal 1.
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That's kind of like saying "if you're working under the assumption that a red object is red". It's a truism. It's not open to debate.
You should realize that you're arguing against logic itself here.
These are the assumptions I'm working under:
http://en.wikipedia.org/wiki/List_of_axioms
Feel free to work under a different set of assumptions to the rest of the world.