Let .999... represent a decimal point followed by infinitely many 9's. Which of the following is true? (And prove it.) Does math make you happy? It should.
.999... < 1
.999... = 1
.999... > 1
Let .999... represent a decimal point followed by infinitely many 9's. Which of the following is true? (And prove it.) Does math make you happy? It should.
.999... < 1
.999... = 1
.999... > 1
Divide by 9 to get 0.111... Notice that this new value is equal to 1/9. Therefore 0.999... = 9 * 1/9 = 1
EDIT: Yes, maths makes me happy, you got a problem with that?
Math oftentimes makes me happy, just not so late at night!
.999... < 1
.999... = 1
.999... > 1
All three are possible answers, depending on what type of math you use, how you round, what the question pertains to, etc, etc. Circumstances, they make the world go round.
Take care all.
MathS makes me cry like a baby. A baby that doesn't like maths.
I like math theory actually, but I don't like doing pages and pages of factoring or whatever it is you want me to do (like err, calculus)
How does 0.9999... > 1 btw? The other two 'proofs' are simple enough.
.999... = 1. The other two are both completely incorrect. .999... is no more less than 1 than 3 is less than 4.
oh, yeah, proof:
there exists no number between .999... and 1, therefore .999... = 1. I don't remember the name of the theorem or law or whatever that says that, but it exists.
Apologies, but I hate and detest maths. I have a head for languages, but not mathematics.
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Oh, GOD, I hate proofs!
I'm so completely rusty, so I wouldn't have to been able to answer that question to save my life. Arche has thoroughly enlightened me.
Darn, doom reminded me that 0.99....is an irrational number, and thus I can't use some sort of pseudo logic to state that 1/9 < 1
*shakes fist*
I hate maths
I'll pick one at random, .999 > 1
The limit of 0.9999.... is equal to one, but 0.999... itself does not equal to one and is alwasy less than one. So I'd say 0.999<1
Some math is cool... I like algebra up to simple calculus, but after that it's no fun... and then applying math to stuff like signals, circuits, and the like is the worst.
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No, this is the only correct answer: .999... < 1 What's there to prove while you can see it.
('-'*)/ - "sup"
About that 1/9 strategy, how can you prove that 1/9 is 0.111... ? You can't use something that has no proof to prove something else of a similar nature like that.
I believe, using the ... strategy instead of the other dot thing, the number between .999... and 1 is 0.0...01.Originally Posted by Doomgaze
Yay?
I should hope you're capable of working out 1/9 on paper and seeing for yourself, BoB You're essentially asking to prove 1/7 is 0.142857142857... with the 142857 pattern repeated infinitely, which is the same principle really. The repeated patterns in 1/9 and 1/7 (and other recurring numbers) occur because of a repeating sequence of remainders to carry over to the next place value when you do the division on each successive place value. Since the remainders repeat, obviously the digits in the answer will have to repeat in exactly the same way once all the place values after a certain point are the same (which is all place values after the decimal point in integers, which will all be 0), and as you've now got a repeating sequence, it's sufficient to show it occurs infinitely
[q]I believe, using the ... strategy instead of the other dot thing, the number between .999... and 1 is 0.0...01[/q]a) I think you mean 0.9...01
b) 0.9...01 is invalid anyway, since the ... means forever, and you can't stick something on the end after forever, otherwise you imply it has an end, which is contradicting the ... in the first place