Math Is Fun Forum

Luckily, this has been done already here

Welcome, Goddess.

Well, I guess that is the thing about mathematics. It's gotta work all the time!

I suppose you read our page on 9 Recurring

Well, let us try with your variation: Does 1 + 0.999... = 2 ?

Let X = 0.999...
   
So, we are asking: Does 1+X = 2 ??

Let's start with: 1+X = 1.999...

Multiply by 10:  10(1+X) = 10(1.999...)
Or: 10+10X = 19.999...

Subtract X from each side to give us: 10 + 9X = 19.999... - X

but we know that X is 0.999..., so: 10 + 9X = 19.999... - 0.999...
or: 10 + 9X = 19
or: 9X = 19-10 = 9
or: X = 9/9 = 1 

So, X is equal to 1 and also equal to 0.999... (because we said so at the top)

Therefore 0.999... = 1

It could work something like this:

Number Each Basket from 1 to 10.

Select 1 Apple from basket 1
Select 2 Apples from basket 2
etc..

You will now have (1+2+...+10) = 55 Apples

If they all weighed 4 oz, then the scales would show 55x4=220 oz.

But if the weight was, say, 225 oz, then you would know that there 5 apples that weigh an extra ounce, so the basket with the heavier apples must be basket 5.

Big smiles here !!

A bit outside my area, but I found a website that has ALL sorts of stuff about harmonic motion which could help here

I may have to change my answer after thinking, but here is my "gut feel":

An even number is, by definition, able to be divided evenly by 2. So any whole number multiple of an even number (the multiple could be odd or even) must also be able to be divided evenly by 2.

In algebra it may go something like this:

A number "x" is even if x=2n, where n is an integer

And a number "y" is odd if y=2m+1, where m is an integer

So, multiplying any "x" and "y" gives: xy=2n(2m+1)

But we know the definition of even is 2 times an integer ...

So, if n(2m+1) is an integer (we may need to prove that ), then 2n(2m+1) will be even, and xy must be even.

Basically just a four sided shape ... have a look at Quadrilaterals

"m" is the gradient of the line. You can read Equation of a Straight Line which is all about "y=mx+b", and also Gradient of a Line which explains how to figure out "m".

Hiya fez ... just "no"? You're just kidding around, right?

Well done, j4tt, of course it is impossible!

Well, amila123, "limits" just mean that if you keep going, where do you end up?

If you start walking fast, then get slower, and slower, and slower, eventually you will be able to figure out that you will never get beyond a certain point. That point is the limit.

It is best to see this by playing with graphs. Try going to these graphs, and choose "reciprocal".

As you move to the right, x increases, but y gets smaller. What if you move very far to the right? x approaches infinity, and y approaches 0. So, the limit at infinity is 0.

Now, that is just an easy example, and there is much more to learn, but the idea is still basically simple.

Well, let's see, on the first day it has x liters, on the second day x(1+2), third day x(1+2+4) fourth day x(1+2+4+8), etc...  Am I on the right track? Any geniuses out there?

Great puzzle, j4tt, but one little problem .... I can't figure it out!! Is there a trick?