easy problem

[DiGiTaIErRoR]

anyone know what 1/9 i.e .111... and .999... =?

[SteveCRM]

what do you mean

[DiGiTaIErRoR]

and means add, +

[DiGiTaIErRoR]

Let me just make my point.

a=.999... repeating forever
b=1
c=.111... repeating forever

it's known that if a+c=b+c then a=b, otherwise a <> b

a+c=undefined, because the result, from the backside, would be 1.111...1110 the 'end'

since you can not define such a solution, b+c, which = 1.111... <> undefined, so .999... <> 1

Tada.

Thank you, thank you very much.

[sql_lall]

Think of the Matrix:
"There is no end" (well actually, there is no spoon, but close enough)

You said that (a + c) has an 'end', however, you also are adding two numbers with an infinite number of decimal, so why their sum would have an 'end' like that i don't know. You should realise that 0.111111... + 0.99999... = 1.1111111....
similar to how
0.11111... + 1 = 1.111111....

It is just that there is no 'backside' to (a+c), 'cos just saying there is implys that there is also a 'backside' to a and c, which you ahve just shown there isn't.

Tada
Thank you, thank you very much.

[bugzpodder]

let me prove you wrong by contradiction DigitalError:

because the result, from the backside, would be 1.111...1110 the 'end'

0.111...+0.999...=1.111...1110 (1)

and RHS has an end. so lets say the RHS has n 1s w/ a single 0 in the end.

now add up

0.111...111+0.999...999 (2)

where there is n 1s and n 9s. you'll get:

1.111...1110, which has n 1s

0.111...=0.111...111+0.000...000111...
0.999...=0.999...999+0.000...000999...

we have a+b=k (1)
and (a+c)+(b+d)=k (2)
k+c+d=k
c+d=0

but c=0.000...000111...
d=0.000...000999...

therefore c+d <> 0

therefore proven by contradiction, 0.111...+0.999...<>1.111...1110, where there is an finite number of 1s in the RHS

[DiGiTaIErRoR]

I never said there was a finite number of 1's, there is not.

The 0 would merely be beyond infinity.

But infinity = infinity, and there would be a 0 there, because infinite significant digits.

Because there are infite digits, you have proven nothing.

[bugzpodder]

by saying that you are implying that infinite is actually finite. there is no "beyond infinity" and there is no "end" to infinity. this is an easy concept to grasp even for high school students like you.

[DiGiTaIErRoR]

But if there's nothing beyond infinity, then not even infinity goes beyond itself.

So you're saying infinite is finite.

[bugzpodder]

actually I was only quoting you DigitalError

infinity cannot be measured because there is no end to it

[DiGiTaIErRoR]

Infinity can be measured.

It's measure is infinite.

Duh.

[sql_lall]

Gee... interesting.
Firstly:
1) Infinity is an idea, not a value. Becuase of this, you cannot 'measure' infinity. And nothing has a measure of infinity, because to measure something you need a start and an end (as bugz said). Something that is infinite could be described as something unmeasureable.
2) Assume there is a 0 at 'the end', past 'infinity'. Then how did it get there?? The two things you are adding together only have an infinite number of digits, so how could there sum have a digit 'beyond infinity' ??? (BTW, this doesn't truly make sense, but i tried to explain it using your terminology)

Finally, some cool stuff to finish with:
3) You said "infinity = infinity"
However, also:
infinity + 1 = infinity
infinity * 2 = infinity
infinity² = infinity
(that is, where this infinity = aleph-0)

P.S. Bugz, you said:
"this is an easy concept to grasp even for high school students like you"
you also are a high-school student though aren't you. In fact, everyone on this post might be. (with the possible exception of SteveCRM)

[bugzpodder]

P.S. Bugz, you said:
"this is an easy concept to grasp even for high school students like you"
you also are a high-school student though aren't you. In fact, everyone on this post might be. (with the possible exception of SteveCRM)

I never said i wasn't.

actually most ppl here (esp those long timers are not high school students) but as far as i am concerned your age makes no difference. Only what you know does.

[marnitzg]

Originally posted by DiGiTaIErRoR
Let me just make my point.

a=.999... repeating forever
b=1
c=.111... repeating forever

it's known that if a+c=b+c then a=b, otherwise a <> b

a+c=undefined, because the result, from the backside, would be 1.111...1110 the 'end'

since you can not define such a solution, b+c, which = 1.111... <> undefined, so .999... <> 1

Tada.

Thank you, thank you very much.

[edit, re-read]
a+c = b+c
or a+(1/9) = 1 + (1/9)
a + (1/9) = (10/9)
a = 1
*** did you prove?

Just because you cannot imagine something, doesn't mean it cannot be done.

Maths was invented by humans. Humans have flaws. Therefore maths has flaws.

[nahya^^]

Write the answer as a fraction, which is 10/9