Don
According to the definition of r there is an infinite string of them that gives it the property of being = 1.
If it didn't equal 1 how do you explain 3 x 0.3r = 0.9r?
Jokester
Poll: Does 0.99 Recurring = 1
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According to the definition of r there is an infinite string of them that gives it the property of being = 1.
If it didn't equal 1 how do you explain 3 x 0.3r = 0.9r?
Jokester
None, AFAIK. It simply depended upon the method of applying to the uni concerned. In my group, I think all but three did BSc, the rest did BA, yet the course was identical.
An infinate number!
Don't imagine a long list of numbers this is no where near infinate, you can always add more 9's onto this list. Instead imagine every 9 possible being there already i.e. they are not continuously being added, they are ALL there now, an infinate number of them
hmmm quite hard to explain.
That FACT that every 9 possible is already there, is the reason it precisely eqauls 1
I fail to see why you are all automatically connecting this 'problem' with maths.
Take 0.3r * 3 = 0.9r
The numbers around the r's in there add up nicely as is obvious to see, but I still maintain that the r part is not definable since it is infinite and therefore has no mathematical use. You are simply saying that infinity times 3 = 3 infinities. Neither of which is a definable number.
Same with w11tho's example:
You've 'defined' the sqrt of 2 as X. Then you've stated that x^2 equals 2. The 'maths' in this case simply tells me that if I take the sqrt of something, I can square it to get the same something I started with. This still doesn't give me a 'mathematical' or 'definite' value for X which you have only defined by substituting it.
You can perform 'mathematical' logic on expressions of infinity and always come up with something that 'figures' within the world of maths, but I still fail to see how doing this proves that infinity is mathematically definable, and can be interpreted as such.
Maths is great and everything but no 'language' in the world can say to me that 0.9r is 1 since the very use of term itself implies that it, and 1, are two different entities.
Without mentioning maths again, I'd like you to prove to me how continually adding 9s onto 0.9 will ever reach, and therefore equal, 1.
Take 0.3r * 3 = 0.9r
The numbers around the r's in there add up nicely as is obvious to see, but I still maintain that the r part is not definable since it is infinite and therefore has no mathematical use. You are simply saying that infinity times 3 = 3 infinities. Neither of which is a definable number.
Same with w11tho's example:
You've 'defined' the sqrt of 2 as X. Then you've stated that x^2 equals 2. The 'maths' in this case simply tells me that if I take the sqrt of something, I can square it to get the same something I started with. This still doesn't give me a 'mathematical' or 'definite' value for X which you have only defined by substituting it.
You can perform 'mathematical' logic on expressions of infinity and always come up with something that 'figures' within the world of maths, but I still fail to see how doing this proves that infinity is mathematically definable, and can be interpreted as such.
Maths is great and everything but no 'language' in the world can say to me that 0.9r is 1 since the very use of term itself implies that it, and 1, are two different entities.
Without mentioning maths again, I'd like you to prove to me how continually adding 9s onto 0.9 will ever reach, and therefore equal, 1.
Don
You do realise that 3 x 1/3 = 1, don't you?
Jokester
Soldato
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0.99
It's going to keep going 9's. That's why it's called reacuring. It's not 1. It's not 0.8. It's just 0.99r.
That's it. Not 1.
Ask yourselfs this. What makes 1.99r 2?
Nothing! Exactly.
It's going to keep going 9's. That's why it's called reacuring. It's not 1. It's not 0.8. It's just 0.99r.
That's it. Not 1.
Ask yourselfs this. What makes 1.99r 2?
Nothing! Exactly.
This is where your understanding is wrong. We are not 'adding' 9s. If we were then yes i would agree that it does not equal 1. The 'r' part however states that every possible 9 is already there, so no more 9s can be added since there is already an infinate number of them. *This* is why it equals 1.
The same thing as 0.9r=1 as described over 29pages
We can "doctor" 0.9r to "add" 9's.
Edit - for anyone who things 0.9r=!1, of course. For others, you prob. know this by heart.
The Gauss formula, for the nth time...
a / (1-r) is the "sum to infinity" of a geometric progression, where...
a is the first term
1 is 1.
r is the common ration, which is the ratio of any two consecutive terms.
Consider 0.9999r to be...
0.9 + 0.09 + 0.009 + 0.0009 +.....
a is 0.9
1 is 1
r is 0.1
0.9 / (1-0.1) = 0.9 / 0.9 = 1.
The series converges to 1. Therefore, 0.9r = 1
lol, of course. but that is still using maths to describe an infinitely detailed number as a 'definite' value by using a symbol to represent it.
It's not like I'm arguing that 1/3, pi, or 0.9r don't exist, i'm just saying that they are all symbols or ways of expressing a value that can't be exactly defined.
It's not like I'm arguing that 1/3, pi, or 0.9r don't exist, i'm just saying that they are all symbols or ways of expressing a value that can't be exactly defined.
Associate
Have a read of this, particularly the bit on "...This is why solids can't pass through one another, why we can't walk through walls...".
Thanks to Alpha and many others for sharing some nice maths and clever thinking through this thread.
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Don
All three can be exactly defined, 1/3 is exactly that, 0.9r is exactly equal to 1, and pi is exactly the ratio of a circle's circumference to it's diameter.
Jokester
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I understand what you are saying and that with this geometric series it appears that you are adding a 9 each time. However this series is an infinate one, since it is infinate every 9 has already been added...** If that makes sense??
EDIT** which is why the a/(r-1) formula works
You're completely missing my point. Think logically, all three of those values are not definable without representing them as a symbol or a term. 1/3 is a representation of an infinitely detailed number. It does exist and it is the ratio of a circle's circumference to it's diameter. I agree with you, but this still doesn't tell me how 0.9r can be 1
Makes perfect sence to me, since I've been shown it explicitly. Some people haven't though , or haven't bothered to read the thread (any or all of it) before casting a vote, so I thought I'd add the proof back to the current page. I wasn't trying to step on your toes, or such.
If you voted not to "1+1=2" you'd be called silly or something, but this seems to be different for no apparent reason.
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