Sven's Official BrainTeaser Thread !! and Sander.

[Mike]

I read the 0.999... proof on the internet, correct. Seeing as there are mathematical proofs for it, it's a theroem.

By writing 0.0, you just show that there's not integer on the position with the value of 1 and 0.1, yes? As you've not written anything on the position of 0.01, you've implied that there's no value for it and thus unnecessery to write a 0 there. It would be a pain in the ass writing 1.000000000000000000000000000000000000000000000000000... evertime you decide that you want to write number 1.

0.0 has no value, just as 0, and thus they're the same number. 1.0 has the value of 1, thus they're the same number.

You can't say that if you write 0.0, there MIGHT be an 1 after the zero, since 0.0 is NOT the same as 0.01.

I want to see a proof of 0.0 not representating the same number as 0, and not by "but if you put a 1 after the zero...", or else you're wrong, because in math, you must ALWAYS put mathematical proofs for every theory so that people can see it's true.

It's like pythagoras theorem, there's a proof for it, and that's why it's true.

[Gustav]

I read the 0.999... proof on the internet, correct. Seeing as there are mathematical proofs for it, it's a theroem.

By writing 0.0, you just show that there's not integer on the position with the value of 1 and 0.1, yes? As you've not written anything on the position of 0.01, you've implied that there's no value for it and thus unnecessery to write a 0 there. It would be a pain in the ass writing 1.000000000000000000000000000000000000000000000000000... evertime you decide that you want to write number 1.

0.0 has no value, just as 0, and thus they're the same number. 1.0 has the value of 1, thus they're the same number.

You can't say that if you write 0.0, there MIGHT be an 1 after the zero, since 0.0 is NOT the same as 0.01.

I want to see a proof of 0.0 not representating the same number as 0, and not by "but if you put a 1 after the zero...", or else you're wrong, because in math, you must ALWAYS put mathematical proofs for every theory so that people can see it's true.

It's like pythagoras theorem, there's a proof for it, and that's why it's true.

I can't give proof for somebody that don't understand math, it's pretty hard

the problem is that 1,0000000000000000000..... is not an exact number, thats the problem, the only way of writing exact 1 is :
1    2/2    3/3    4/4 etc

[Sander]

mike, finally i agree with you  :cheers:

(about the 0,0 thing though), 0,9999999 still isn't one and will never be so.

and sven, can you change the title of the tread? 'mathematical discussions about decimals' is a good title  :biggrin:

[Mike]

Gustaf, give it a try, i'm doing it all the time for you.


1.000... with infinitely number of 0's is 1, since you've put a zero on every position of every value <=10^-1.

If your method is correct, then numbers are devisable with 0.0, since it's a bit higher than 0 (numbers arn't devisable by 0, though by >0 and <0.). Try devide 1 with 0.0.

Great Sanders :thumbsup: . 0.999... = 1 , though, will always be.

[Gustav]

Mike, if you put 0es forever after 1, it will not be thesame as 1 because you've changed it , it's not a concrete number because it will never end,

0,0 is not an exact number, the decimals tells it isn't

[Mike]

Writing 1 implies an infinite sequens of zeros after the 1, as you havn't put any value to the positions after 1, no value for a position = 0. It's just as writing 1 implies you have no value for the position of 10, 100, 1000, and thus nobody write 0001, when writing 1.

0.0 is exact 0.0, because of the implication that there's no value for any other position. Thererfore 0.0 is an exact number.

[Sander]

okay gustav, it's not an exact number, i agree. but still it's zero, only rounded off, because it's something like 0,000000001. it's just a rounded off number. therefore 0 is not 0,0. and i know i've said it's the same but i take that back

[Mike]

0 could then just as well be a rounded of 0.1.

How on heavens earth could 0.0 be 0.0000001?

[Gustav]

Writing 1 implies an infinite sequens of zeros after the 1, as you havn't put any value to the positions after 1, no value for a position = 0. It's just as writing 1 implies you have no value for the position of 10, 100, 1000, and thus nobody write 0001, when writing 1.

0.0 is exact 0.0, because of the implication that there's no value for any other position. Thererfore 0.0 is an exact number.

If you wan't to define an exact number you can just say that there can't be any decimals after it... the decimals always makes the number change from what it is

[Mike]

There's no such definition of an "exact number"

Read this instead:

http://en.wikipedia.org/wiki/Number#Integers

Go to "real numbers".

[Sander]

0 could then just as well be a rounded of 0.1.

How on heavens earth could 0.0 be 0.0000001?

10,4/999999999 is a very small number. agree?
when the 10,4 is rounded off, the answer can have only 3 digits (significance rule, don't know if you ever had that)
therefore the answer can be only 3 sign. nrs because the 10,4 is only 3. so 0,000000001 something will be rounded off to 0,00. although you know the answer is more than 0

[Mike]

We're not discussing about 0.0 and 0 in terms of rounding of.

But with your logic;

-0.5<=0>0.5
-0.05<=0.0>0.05
-0.005<=0.00>0.005

then 0 is most likely to be > 0.0