Walter Wayne
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Not true. .999... squared is .999... no matter how many times you do it.Dorian Gray said:
Edited to add: but that is for the other thread.
Walt
Are there unquestionable answers?
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Edited to add: but that is for the other thread.
Walt
Yes. Absolutely and unequivocally. They are two different notations for exactly the same number.
Not correct. No matter how many times you square 0.999... it will always equal 0.999...
You may benefit from reading the thread cited previously by LW.
Edited to add: I see Walter beat me to it.
Dorian Gray
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Virtually the same, but not exactly the same.
Dorian Gray
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x = .99999.....
10x - x = (9.99999... - 0.99999...) distributes out in the following ways:
x(10 - 1) = 0.99999...(10 - 1),
x = 0.99999......
10x - x = (9.99999... - 0.99999...) distributes out in the following ways:
x(10 - 1) = 0.99999...(10 - 1),
x = 0.99999......
1/9 + 8/9 =9/9=1
1/9=0.11111(repeated infinitely)
8/9=0.88888 (repeated infinitely)
.88888(repeated infinitely) + 0.11111(repeated infinitely) will always be 0.99999 (repeated infinitely)
You can do this with 2/3 and 1/3 or 3 x 1/3 or any two fractions that have the 9 in the denominator that will add up to 9/9---no matter how you do it you will always get 1 on one side and 0.999999 repeat on the other --multiple lines of evidence all leading to the same thing is very strong evidence that the result need not be questioned..They are equal--not nearly so or very close to the same--in our numbers system they are the same---(Neutrality and infinity or two concepts that are very hard for many to understand)
1/9=0.11111(repeated infinitely)
8/9=0.88888 (repeated infinitely)
.88888(repeated infinitely) + 0.11111(repeated infinitely) will always be 0.99999 (repeated infinitely)
You can do this with 2/3 and 1/3 or 3 x 1/3 or any two fractions that have the 9 in the denominator that will add up to 9/9---no matter how you do it you will always get 1 on one side and 0.999999 repeat on the other --multiple lines of evidence all leading to the same thing is very strong evidence that the result need not be questioned..They are equal--not nearly so or very close to the same--in our numbers system they are the same---(Neutrality and infinity or two concepts that are very hard for many to understand)
What do you mean by that? I know the definitions of the words you used, but I'm not getting your point.
Wouldn't this conversation be more appropriate in the other thread instead of hijacking this one? If you don't agree that 0.999... is exactly equal to one, then I'd like to politely insist that you read that other thread before making any further comments.
All that stuff has already been posted ad nauseum in that other thread. No need to repost it here.
phildonnia
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Re: Re: Re: Are there unquestionable answers?
I think Descartes meant "Cogito Cogito Ergo Cogito Sum."
(or "ITITTITIA")
Keneke said:
I think Descartes meant "Cogito Cogito Ergo Cogito Sum."
(or "ITITTITIA")
Dorian Gray
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A discrete fraction isn't exactly equal to a repeating decimal, either. I can give you 1/9 of something, but I can only approximate giving you .11111........ of something.
Which is also why 1 >< .99999.....
Which is also why 1 >< .99999.....
Dorian Gray
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Okay, I will show off my unbelievable ignorance in that topic.
Thanks for the advice, X.
But there are no unquestionable answers.
Thanks for the advice, X.
But there are no unquestionable answers.
Underemployed
Muse
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Robotman put it this way: "'I think I think, therefore I think I am, I think' - the guy was a lot more insecure than history portrayed him."
Here's an unquestionable answer: Yes, you are going to die.
Here's an unquestionable answer: Yes, you are going to die.
evildave
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1=1 ... One what? What units are we using? One orange and one orange? Are any two oranges equal? By weight? By flavor? By texture?
0=0 ... Zero what? Do we really ever have zero of anything? Zero gravity? Zero atmosphere? The closest thing you have here is a convention, setting a requirement for a 1998 Toyota pickup truck in your living room, you might say there are zero. You might yet say there are zero 1998 Toyota pickups if you have a 1999 Toyota pickup in your living room, but for most requirements of pickup truck in living room, any old model year, or even model pickup truck will generally do.
True=True or False=False is simply by convention of definition. Most people over, or under-qualify or otherwise botch the prepositions for true or false in a given situation. Just because you can blubber something half-remembered about equation from your grade school algebra/geometry, doesn't mean that true or false relate to anything you're trying to demonstrate.
As for the decimal fractions, it's only one kind of approximate representation of values. Even most programmers use floating point (not the same as real) without realising what a mess a 32 bit floating point value is. They'll merrily use it for location, not realising that it represents extreme precision near the origin, while absurdly poor resolution far away from it (i.e. 1.3 units is not the same as 1000000.3 units). Using floating point values for position is the same as never really knowing where it is. A representation of 1/3, instead of 0.3333... can be used to do a little math to come up with a function that defers division until later, and that will always yield better results than sticking to floating point values from the beginning (assuming you did the math right and checked the results). Not always important, but occasionally critical.
As for, "Yes, you are going to die!", this doesn't really answer anything. Yes? Really? When? How? What is death for you, personally? A tunnel with angels on the end? Lights out? What? Are you dead when you're still on life support, and the doctor can't get any reaction from you, or might that be a spinal injury?
0=0 ... Zero what? Do we really ever have zero of anything? Zero gravity? Zero atmosphere? The closest thing you have here is a convention, setting a requirement for a 1998 Toyota pickup truck in your living room, you might say there are zero. You might yet say there are zero 1998 Toyota pickups if you have a 1999 Toyota pickup in your living room, but for most requirements of pickup truck in living room, any old model year, or even model pickup truck will generally do.
True=True or False=False is simply by convention of definition. Most people over, or under-qualify or otherwise botch the prepositions for true or false in a given situation. Just because you can blubber something half-remembered about equation from your grade school algebra/geometry, doesn't mean that true or false relate to anything you're trying to demonstrate.
As for the decimal fractions, it's only one kind of approximate representation of values. Even most programmers use floating point (not the same as real) without realising what a mess a 32 bit floating point value is. They'll merrily use it for location, not realising that it represents extreme precision near the origin, while absurdly poor resolution far away from it (i.e. 1.3 units is not the same as 1000000.3 units). Using floating point values for position is the same as never really knowing where it is. A representation of 1/3, instead of 0.3333... can be used to do a little math to come up with a function that defers division until later, and that will always yield better results than sticking to floating point values from the beginning (assuming you did the math right and checked the results). Not always important, but occasionally critical.
As for, "Yes, you are going to die!", this doesn't really answer anything. Yes? Really? When? How? What is death for you, personally? A tunnel with angels on the end? Lights out? What? Are you dead when you're still on life support, and the doctor can't get any reaction from you, or might that be a spinal injury?
To clarify, sometimes a decimal representation is an approximation (irrational numbers, for example), but sometimes it's an exact value. For example, the decimal notation 0.333... is not an approximation. It is an exact value. Anytime the repetend of a decimal expansion is completely specified, it is an exact value, not an approximation.