Poll: Does 0.999.. equal 1 ?
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Ok take this logic
If you take the limit of y=(1/2)^x where x goes to infinity, you get 0
Logically, it wouldn't matter what fraction was inside the parentheses as long as it was between 1 and 0, y=(.1)^x would work equally as well
Is it not true that .1=.1^1? or .01=.1^2? or .001=.1^3?
Following this pattern, the decimal can be represented as .1^x where x is the number of zeros in between the final digit and the decimal point, minus 1
Now, if I gave you the number .(0)1, where its infinite zeros followed by 1, would it not be represented by the function .1^(∞-1)? Isn't ∞-1 the same as ∞ for the purposes of algebra? So it could also be represented as .1^∞.
Haven't we proven that in a case of finding the limit of y=(.1)^x where x goes to infinity the answer is always 0?
So logically, .(0)1=0.
Now, what is 1-.(0)1?
Wouldn't it be .(9)?
So, .(0)1=0,
1-.(0)1=.(9)
1-0=.(9)
1=.(9)
If you take the limit of y=(1/2)^x where x goes to infinity, you get 0
Logically, it wouldn't matter what fraction was inside the parentheses as long as it was between 1 and 0, y=(.1)^x would work equally as well
Is it not true that .1=.1^1? or .01=.1^2? or .001=.1^3?
Following this pattern, the decimal can be represented as .1^x where x is the number of zeros in between the final digit and the decimal point, minus 1
Now, if I gave you the number .(0)1, where its infinite zeros followed by 1, would it not be represented by the function .1^(∞-1)? Isn't ∞-1 the same as ∞ for the purposes of algebra? So it could also be represented as .1^∞.
Haven't we proven that in a case of finding the limit of y=(.1)^x where x goes to infinity the answer is always 0?
So logically, .(0)1=0.
Now, what is 1-.(0)1?
Wouldn't it be .(9)?
So, .(0)1=0,
1-.(0)1=.(9)
1-0=.(9)
1=.(9)
There's no such thing as "one less than infinity". Either it's infinitely many or there's finite number, which is followed by another finite number and not infinity.Winthrop said:
There's yet to be a correct proof from someone who claims they're not the same, and multiple proofs from the ones saying they are. But I guess it's easy to argue you're correct if you ignore proofs.
The proofs all use rounding errors. I personally know mathematicians who have proven those wrong. for instance 1/3 is not .33333 it is approximate. ((.99...)10)-.99.. = 8.99...1 not 9. I have not seen one of these proofs that does everything correctly. They need an approximation in the equation rather than an equals sign or it fails to be correct, and an approximation would not prove that .99... = 1karplas said:
Actually that is real life. If you're measuring distance up to an infinite point, you can't reach it. That's the point of infinite.maninahat said:
Remind me, what is 0.(9) as a fraction? Because 1/3*3 is 1. That's the point of decimalising fractions, or fractionalising decimals, you store the tolerance. Infinitely small measurements are treated as 0, but they still hold measure.
But then, repeated posts on a subject that has an official answer and a differing scientific answer are always good for post boosting. See the Triple Point of Water, How Many Moons does Earth have, Is Pluto a Planet and others.
Lets give the number you mentioned X. Depends on situation, and of the order of magnitude of 1 - X (the number you gave). In most cases X equals 1 for all intends and purposes if 1 - X is somewhere in the order of magnitude of tenth to the minus 6 power. (1 divided by a million).
For Math, no it doesn't equal math and thats why math suck. Physics is better, and there it can equal one.
For Math, no it doesn't equal math and thats why math suck. Physics is better, and there it can equal one.
Protip: Infinity minus 1 is still infinity, Subtraction does not make it a finite numberWinthrop said:
I remember in the last post of this (There have been so fucking many) someone who actually understood maths pointed out how for the maths to work probably you must add a number to the end.
So 1.111... should be 1.111...1.
Even if it has no end, you have to assume it ends somewhere for it to work. Maths is not flawed, but the concept of infinity is.
So 1.111... should be 1.111...1.
Even if it has no end, you have to assume it ends somewhere for it to work. Maths is not flawed, but the concept of infinity is.
If you're referring to the 1/3 = 0.(3) etc. proof, I would like to agree with a quote from Wikipedia:mps4li3n said:
I'm in my first year of mathematics at university, so I can safely claim I have 'any math knowledge'. It doesn't make me a mathematician, but I've come to realise that many concepts we believe being trivially true actually are quite complex when mathematical rigor comes in.
How about my proof, then? If the two were different real numbers, by the density property, there would be an infinite number of other real numbers between them. No such numbers can be found. Thus, they must represent the same number.Winthrop said:
Yes.
x=0.99... recurring.
100x=99.99... recurring.
100x-1x=99 so 99x=99
99x=99 divide all by 99.
x=1.
x=0.99... recurring.
100x=99.99... recurring.
100x-1x=99 so 99x=99
99x=99 divide all by 99.
x=1.
no, your calculator would have said it was 0.3333333, or 0.33333333333333 or 0.3333333333333333Zukhramm said:
depending on how many digits your screen could display, or the bit width of the calculators registers...
it didn't say it was 0.3recurring! just as it says 1, and not 0.9recurring!
the fact that 0.3333333333 'looks' a lot more like 0.3recurring, than 1 'looks' like 0.9recurring, doesn't mean anything!
as far as I'm concerned 1/3 = 0.3recurring should be no more or less questioned than 1 = 0.9recurring.
0.999 is closer to 1 than 0.33 is to 1/3
By definition, it does (0.9... anyway, not 0.9999). There cannot exist proofs both for and against the same thing, so the proofs at that link are necessarily false; sadly I don't have time to pick over them in detail.Winthrop said:
BTW, anyone attempting addition, multiplication, subtraction or division on a recurring decimal may just as well divide by zero.
That's an equivalency operation, and not a valid proof.
That's an equivalency operation, and not a valid proof.