0.99r = 1

I'm sort of mixed on this: If you take a definition of infinity as that "value" for which a series becomes its limit, then by definition: 0.9r = 1. It's a tautology. I don't think that's very interesting, although I'm not sure how else you would define infinity...

edit: I didn't think much of the video by the way - it glosses over some deep ideas and challenges in a very breezy manner!
 
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It's not equal to one because it's infinite, anything else is mathematical trickery or cheating, you see because it's infinite you can't ever finish doing the calculation and of course because it's infinite you won't ever get to a point where it magically becomes one.
 
Radiation said:
It's not equal to one because it's infinite, anything else is mathematical trickery or cheating, you see because it's infinite you can't ever finish doing the calculation and of course because it's infinite you won't ever get to a point where it magically becomes one.
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It is not trickery at all and the fact that the recurring decimal is infinite doesn't change anything.
What is one third + one third + one third? The correct answer is one but you are claiming since 1/3 has an infinitely recurring decimal that the answe is not one. You are wrong. Accept it.

Similar question, what is 1/3 * 3? The correct answer is funnily enough 1 but you are claiming it wouldn't be.


Funny how the only people that think otherwise don't have a maths education beyond GCSE yet seem to think their incorrect opinion iris right despite what every mathematician or half intelligent human has ever said.
 
AGD said:
I'm sort of mixed on this: If you take a definition of infinity as that "value" for which a series becomes its limit, then by definition: 0.9r = 1. It's a tautology. I don't think that's very interesting, although I'm not sure how else you would define infinity...

edit: I didn't think much of the video by the way - it glosses over some deep ideas and challenges in a very breezy manner!
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You are right, it is a tautology basically, that is why it always has to be true. That is the way it is defined.

The best way to view it is by looking at the fractions. 1/3 = 0.3r.
These are all just symbols to represent the same entity. Some people just cannot accept that you can have 2 different symbols meaning the same thing.

The question basically boils down to:
X = 42
Y = 42

Does X=Y? Of course but Lots of people seeming to think that 2 numbers with different symbols somehow don't mean the same thing:rolleyes:
 
D.P. said:
It is not trickery at all and the fact that the recurring decimal is infinite doesn't change anything.
What is one third + one third + one third? The correct answer is one but you are claiming since 1/3 has an infinitely recurring decimal that the answe is not one. You are wrong. Accept it.

Similar question, what is 1/3 * 3? The correct answer is funnily enough 1 but you are claiming it wouldn't be.


Funny how the only people that think otherwise don't have a maths education beyond GCSE yet seem to think their incorrect opinion iris right despite what every mathematician or half intelligent human has ever said.
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My point still stands amazingly enough, you see if you want to say 1/3 as .3r then no you could never do the calculation as it's infinite, you're using a different kind idea to get a result, you can use thirds when you slice a cake and it works but if you're talking about real math and say .3r then no 3 x .3r won't ever be one. :)
 
D.P. said:
It is not trickery at all and the fact that the recurring decimal is infinite doesn't change anything.
What is one third + one third + one third? The correct answer is one but you are claiming since 1/3 has an infinitely recurring decimal that the answe is not one. You are wrong. Accept it.

Similar question, what is 1/3 * 3? The correct answer is funnily enough 1 but you are claiming it wouldn't be.


Funny how the only people that think otherwise don't have a maths education beyond GCSE yet seem to think their incorrect opinion iris right despite what every mathematician or half intelligent human has ever said.
Click to expand...

It's a well documented psychological thing: Dunning-Kruger Effect. Summary: the less qualified you are to opine on a given subject, the more confidence you will place in those opinions.
 
lukeharvest said:
It isn't 10-0.999..., it's 9.999r - 0.999r. Besides, that's by far the weakest proof of 0.999... = 1 because you can question manipulating infinite decimals. A much better proof is expressing 0.999... as a sum

9(1/10) + 9(1/10)^2 + 9(1/10)^3 + ...

Which is clearly 0.999...

You can then use the sum of an infinite geometric series to get the answer as 1.
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Makes more sense than what she said, indeed. Thanks.
 
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