Poll: Does 0.999.. equal 1 ?
- Thread starter mattsipple4000
- Start date
Recommended Videos
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.
There is a substantial difference between infinity minus 1 and one less than infinity. Infinity is not a number therefore it cannot be subtracted. You are right that one less than infinity is still infinity however it is a different infinite set and cannot be compared with the old infinite set.Spencer Petersen said:
I never claimed my calculator said 0.3 recurring. The fact that it did not was what made me learn that 1/3 = 0.333... because as I devided one by three, I tried to return to one by multiplying it with three again and ended up with a bunch of nines on the screen. I asked my parents about it and got the answer that it was because the calculator could not handle an infite amount of numbers and therefore made a small error.matt87_50 said:
Implying that the set of decimals will end 1 digit before the other set is also implying that either one will end at some point. Because they are infinite they will never end.Winthrop said:
I agree the proofs which work with statements like 1/3=0.(3) do not actually give new insights, but only show that the statement 1/3=0.(3) is equivalent to 0.(9)=1. However, I'd like to know what proof(s) you (or the mathematicians (what are their credentials by the way?) you know) can give that "1/3 is not .(3)".Winthrop said: