Fun maths problem

Who can prove that " 0.999... = 1 "

(infinite nines after the comma)

 

Umm, Ill take a crap with my very limited math skills.

all the numbers divided by themselves equal one, or you estimate (not likely, but hey)

 

Oh, that old trick. Here watch this, see nothing up my sleeves? good.

Let X = 0.9 recurring

Multiply both by 10 to get:

10X = 9.9 recurring

Note that after the decimal point both RHS are the same, that is for any decimal place they both contain 9 and so we subtract one from the other to cancel them out completely and since it is just 1 copy of the 0.9 recurring it is also just one copy of X to get:

9X = 9

Divide both by 9:

X = 1

and going back to the start we get

1 = X = 0.9 recurring

I'm no Tom Lerher but I'm easier to follow

 

No, because you are in reality multiplying with 0,9, which you will have to do on both sides of the equal sign, so that you get:

9X = 8,999...

Tom Lehrer's math is perfectly logical, by the way:

Code:

 342   342
-173  -173
=169  =147

 

next one, who can mathmaticly proov that women are evil

 

That is easy:
First we assert, that girls require time and money:

Girls = Time X Money

As we all know, time equals money:

Girls = Money X Money

Money, as we know, is the root of all evil:

Girls = sqroot(Evil) X sqroot(Evil)

This leads us to the answer, that:

Girls = Evil

 

No. It's mathematically correct and there isn't any multiplication by 0.9 just subtraction of the first equation. It's the same procedure use to convert decimal rational numbers to fractional representation.

Think

Code:

  9.9999999999...
- 0.9999999999...
_______________
  9.0000000000...

On the other side it's the same except since I declared 0.9 recurring to be equal to X it's simply

Code:

10X - 0.9999999999...
10X - X
9X + X - X
9X

I know the end result of this gives people a lot of trouble. The decimal representations for some numbers aren't unique. If you need any more convincing I'd suggest you read a good text book.

I know, but he presents it at such speed that it is a little difficult to keep up.

 

No, it isn't. What you are referring to, is that nine ninth is the same as one, which is correct, but you are misrepresenting it. 0,9r is not the same as nine ninth, because the 'final' one in 0,1r in one ninth (i.e. the last one for any written length of the division one ninth) is not the result of the division, but one carried. Likewise, one third does not equal 0,3r, but 0,333...1, which is easier to see than for the one ninth example, because of the difference in digits. Perform the operation on paper, if you don't trust me - no matter how far you get, you still have to carry the one. Therefore, nine ninth is in fact 0,9r + 0,000...1, which is not what you wrote.

My calculation is therefore correct.

As for Tom Lehrer, I don't find him hard to follow at all:

 

Did you hear that whoosh? That was the sound of something going completely over my head..... :lol:

 

??????

My God, glad I left School at 14!!! Pass! Pass! Pass!
but.... question for you...
"Why is a mouse when it spins?"

 

a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1


i will post the answer if anyone wants to see it

 

A = B - Yes
A^2 = A * B - Yes
A^2 - B^2 = A * B - B^2 - Yes
(A + B) * (A - B) = B(A - B) - Yes
(A + B) = B - No - you are multiplying with (A + B) or B^2 on one side, and B on the other, in the example above, so you can't simply remove (A - B) in both cases.

 

Would you believe that after reading that, and rereading it I still have no idea what you're on about.

To start with, what on earth is "nine ninth"?

 

Yes it is.

The first example is correct. The second is not.

 

Only problem with that Chris, is that the quotation is.... "The love of money is the root of all evil".

So you need to add love to your equation, re-write it, balance it, & Bob's your Uncle!

 

It is, because the book wants you to do it in Base-8.

I must agree with Gryle here though. I may not be a bright bulb in mathematics (and there goes my credibility in this thread), but that doesn't really explain why I can follow his explanation but not Christian's.

 

O.K.

In base 10 (Which we all use, don't we?) the first example was correct. The second not.

Linked question.
Apart from digital equipment which uses base 2. Are there any other bases in common use?

 

I find it hard to formulate it correctly, but Gryle simply CAN'T be correct.
By this same method you could also make 0.777777=1
Continuing this path you can make everything equal 1.
Which means that if I wish to travel around the world 50 times I'd only have to walk 1 mile/inch/meter/whatever and I'm done, since everything equals 1.

Tom Lehrer is in fact correct, if you use the correct base (though why you would use any base beyond 2 or 10 is a bit beyond me as well).

 

Gryle
It may be nine ninths, I'm not entirely sure. In any case, it's one, divided by nine, multiplied with nine.

Basically, one ninth can be represented as 1 / 9 or 0,1r (i.e. 0,111... - 0,1r is the mathematically correct nomanclature for an infinitely recursive string of numbers). As mentioned for one third (1 / 3), when you divide one by three, you will have to carry the one from the division infinitely, and thus 1 / 3 does not equal exactly 0,3r - there will always be a remainder of one.

The same is true in the calculation being made when attempting to prove that 0,9r = 1, although in a different way. Subtracting one from ten, of any given unit, is mathematically the same as subtracting 10 % or multiplying with 0,9. Therefore, the result of your third step should be that 9X = 8,999...1, and not 9X = 9.

I found a similar explanation at <http://forum.physorg.com/index.php?showtopic=13177&st=0>

David

That depends on your definition. The one you gave is the original one, but not the most commonly used one.

Hexadecimal numbers (base 16) is very common in coding and programming. Octal numbers (base 8) also have practical applications.

 

The commonly-used ones being mis-quotes...


The Babylonians apparently used a base-12 system, though it is no longer in common use.