Sven's Official BrainTeaser Thread !! and Sander.

[Sander]

x=0.999...
10x=9.999...
10x-x=9.999...-0.999...
9x=9
x=1
1=0.999...

1/9=0.111...
9*1/9=9*0.111...
9/9=0.999...
1=0.999...


Something, which is infinitely close to something, is just right on it. 0.3999...=0.4 i.e

i've thought about these and i found arguements ;)

when x= 0,99999....
then 10x=9,9999.... with one 9 less after the dot!!! x has infinite nines after the comma, 10x has infinite-1
so you get something like: 10x-x=9x=9,9999...990- 0,9999...999= 0.0000000....01
and because that equals to 9x, it must be devided by 9, so it gets even smaller

second one of you:
1/9=0,111111 (it's an infinite amount of ones because the number is rounded off, so there's a little bit more)
9*1/9=0,1111111*9=1 because you rounded the numbers off, so you get 0,999999. but you miss again 0,000001/9, what makes the answer 1

1=1, when other numbers are in the equation, other ones must substract or add something from/to the number to make it one.
3-2=1
0,4+0,6=1
0,999999...+0,0000001...=1
it's the bold number you keep forgetting. your equations look correct at first sight, but are wrong because you forget the number in bold ;)

[Mike]

If you take something away from an infinity, there's still an infinity left. So in x and 10x, there are exactly as many decimals of 9.

You can apply it to 0.888...
x=0.888...
10x=8.888...
10x-x=8.888...-0.888...
9x=8
x=8/9
0.888...=8/9, which is true, right?

You can try it for any number with an infinite sequense of decimals, it'll always give you the fraction number.

to get 1/9 you'll need an infinite sequence of the number 1, nothing rounded up. so you actually have 0.1+0.01+0.001+0.0001... and so on. multiply that with 9 and you'll get 0.9+0.09+0.009+0.0009... and so on, thus 9/9=1.

Oh, btw. 0.0=0 and will always be.

How numbers are built up; let's take 1234,567 as an example.

number 4, stands for 4. 3 is though worth 10, so it stands for 3*10, 2 is worth 100 so it stands for 2*100 and so on. Working backwards, 5 stands for a decimal worth 0.1, so it's worth 5*0,1, number 6 = 6*0.01 and so on.

So 0.0 will then be 0*1+0*0.1=0
1.0 = 1*1+0*0.1=1

0.0=0
1.0=1

there's not really much to argue about there...

[SvenF]

[...]
Oh, btw. 0.0=0 and will always be.

How numbers are built up; let's take 1234,567 as an example.

number 4, stands for 4. 3 is though worth 10, so it stands for 3*10, 2 is worth 100 so it stands for 2*100 and so on. Working backwards, 5 stands for a decimal worth 0.1, so it's worth 5*0,1, number 6 = 6*0.01 and so on.

So 0.0 will then be 0*1+0*0.1=0
1.0 = 1*1+0*0.1=1

0.0=0
1.0=1

there's not really much to argue about there...

You're right, but I think it's evident that 0.0=0. :thumbsup:

[Gustav]

Mike, you can't say that 1,001 is thesame as 1 you have to do like this, 1,001~1 .. 1,00~1 is thesame works thesame way , when you have decimals it's another number, that's why you have them ,

1 is an exact number 1,0 is not.

[Royal Freakiness]

Mike, you can't say that 1,001 is thesame as 1 you have to do like this, 1,001~1 .. 1,00~1 is thesame works thesame way , when you have decimals it's another number, that's why you have them ,

1 is an exact number 1,0 is not.

that's exactly what I was thinking
 :cheers:

[GrIzz]

Mike, you can't say that 1,001 is thesame as 1 you have to do like this, 1,001~1 .. 1,00~1 is thesame works thesame way , when you have decimals it's another number, that's why you have them ,

1 is an exact number 1,0 is not.

Gustav got it right.
I fully agree wtih gustavs explaining.
There can't be a decimal after wich is 0 after and number and end.
can't be written 1,0000,- thats why we call it 1 beacuse it's an exact number.
If you add the decimal 0 after there must be more, beacuse it's not an exact number.

But i understand the other versions aswell, but i don't see them as correct.
Convince me otherwise if you can.

[SvenF]

Ok I try to explain it how I think it is.

Mike, you can't say that 1,001 is thesame as 1 you have to do like this, 1,001~1 .. 1,00~1 is thesame works thesame way , when you have decimals it's another number, that's why you have them ,

1 is an exact number 1,0 is not.

1,001~1: Thats correct because the last decimal number is a 1; 1,001 is approximately the same as 1. As if you take 1 piece of a cake for example. But if you take 1,001 pieces of cake, you got a small amount more than 1 piece, but you can negligate it because it is only a small crumb of cake. However it is not the same amount, that's why you write an '~'.

1,00~1: This is wrong (I think at least it is) because 1,00 is exactly the same as 1. If you eat 1 piece of cake you eat as much cake as if you eat 1,00 piece of cake. Or if you say that you've got 1€, you can also say or write that you've got 1.00€.
In physics we learned that you use decimal numbers to precise your mesures. (It makes no sense to mesure in athletics for example that someone ran 100 meters in 10,1275013 seconds.) However if you say he ran 100 meters in 10,00s, you want to say that he ran it in exactly 10 seconds, and not 10,01, because in this case it makes a difference if he ran 10,00s or 10,01s. You want to precise that you did not round down(?)/off(?) 10,01, but it was exactly 10. What I want to say is that 10,00, or in our case 1,00 is exactly the same as 1. If you want to say that it was 1,001, you write that it is 1,001, and not 1.
Moreover, in shops it is always indicated 1,00€ to precise that it's exactly one euro, and not some cents more. At least in my country they do not write 1€ on the pricelabel.

I hope you understand what I mean, and that I cleared you guys how I think it is. :thumbsup:

[Gustav]

Ok I try to explain it how I think it is.

Mike, you can't say that 1,001 is thesame as 1 you have to do like this, 1,001~1 .. 1,00~1 is thesame works thesame way , when you have decimals it's another number, that's why you have them ,

1 is an exact number 1,0 is not.

1,001~1: Thats correct because the last decimal number is a 1; 1,001 is approximately the same as 1. As if you take 1 piece of a cake for example. But if you take 1,001 pieces of cake, you got a small amount more than 1 piece, but you can negligate it because it is only a small crumb of cake. However it is not the same amount, that's why you write an '~'.

1,00~1: This is wrong (I think at least it is) because 1,00 is exactly the same as 1. If you eat 1 piece of cake you eat as much cake as if you eat 1,00 piece of cake. Or if you say that you've got 1€, you can also say or write that you've got 1.00€.
In physics we learned that you use decimal numbers to precise your mesures. (It makes no sense to mesure in athletics for example that someone ran 100 meters in 10,1275013 seconds.) However if you say he ran 100 meters in 10,00s, you want to say that he ran it in exactly 10 seconds, and not 10,01, because in this case it makes a difference if he ran 10,00s or 10,01s. You want to precise that you did not round down(?)/off(?) 10,01, but it was exactly 10. What I want to say is that 10,00, or in our case 1,00 is exactly the same as 1. If you want to say that it was 1,001, you write that it is 1,001, and not 1.
Moreover, in shops it is always indicated 1,00€ to precise that it's exactly one euro, and not some cents more. At least in my country they do not write 1€ on the pricelabel.

I hope you understand what I mean, and that I cleared you guys how I think it is. :thumbsup:

it can be a 1 after 1,00, you don't know it, ... it can zeroes forever after 1,00 and it will never end, then it's also a bit,bit higher then 1,

1, is exactly 1,  1,00 is not exactly one it's a bit higher

[Mike]

The number zero defines that there's no value for the number worth 10^n.

you have to see how numbers are built up; 103=1*100+0*10+3*1. The zero says that the number on the value worth 10 is zero.

So if you write 0.0, you have stated that the number on the value of 1 is zero, and the number on the value of 0.1 is zero as well.

If you take two numbers and subtract one from the other, and 0 remains, they are equivalent, right?

1-1.0=0        The same

1-1.001=-0.001   Not the same.

Though 1.0 is not the same as 1.001

1.0 - 1.001 = 0.001  Not the same.

1.0 is just a more precise way of expressing 1. If someone asks you how much money've you got (in millions)? And you have one million dollars, you'll answer one million. Saying one million will make him think you rounded it up or down, so you can either be having 1.499...(1.5) or 0.5 millions dollars, but if you say 1.0 million dollars, he knows you're closer to 1 million than you were when you said 1 million dollar(1.04999...(1.05) or 0.95).

1.0=1, just as 03=3 (nothing on the position with the value of 0.1 and 10)

1=1.000... with an infinity sequens of zero's anyways.

And everything roy said is true.

This is math btw, so if you claim something, you can ALWAYS put up mathematical proofs for it. That's the beauty of it.

[SvenF]

I like how you express what you want to say Mike. Good explanation.

[Gustav]

The number zero defines that there's no value for the number worth 10^n.

you have to see how numbers are built up; 103=1*100+0*10+3*1. The zero says that the number on the value worth 10 is zero.

So if you write 0.0, you have stated that the number on the value of 1 is zero, and the number on the value of 0.1 is zero as well.

If you take two numbers and subtract one from the other, and 0 remains, they are equivalent, right?

1-1.0=0        The same

1-1.001=-0.001   Not the same.

Though 1.0 is not the same as 1.001

1.0 - 1.001 = 0.001  Not the same.

1.0 is just a more precise way of expressing 1. If someone asks you how much money've you got (in millions)? And you have one million dollars, you'll answer one million. Saying one million will make him think you rounded it up or down, so you can either be having 1.499...(1.5) or 0.5 millions dollars, but if you say 1.0 million dollars, he knows you're closer to 1 million than you were when you said 1 million dollar(1.04999...(1.05) or 0.95).

1.0=1, just as 03=3 (nothing on the position with the value of 0.1 and 10)

1=1.000... with an infinity sequens of zero's anyways.

And everything roy said is true.

This is math btw, so if you claim something, you can ALWAYS put up mathematical proofs for it. That's the beauty of it.

Actully, what you talking about there has nothing to do about the thing we are talking about.. it's not about this, take it another time

But your math is wrong man .. you round numbers to numbers that they not are. ..  that's the problem so you have no proofs at all , just theorys that you've read on internet..

you can't say that 1-1.0=0  it's 1-1.0=0.0

[GrIzz]

Decimals are there for concluding that there is more to the number than one.
If you then take 1,00 in my sence it concludes that there are more to this number than just 1.
Why split up 1 into 1.00 in the first place if you mean 1.
1 is 1, not 1.00
Decimals are there for a reason, if you put on decimals it indicates/state that there is more to the 1 thats allready there.

Well my opinion