math riddles...

[Dogbert]

Simple (non scientifice) way:
1. Take a calculator
2. type: 0.999999999 [+] 1 =
3. type: - 1 =

Most calculators will round it up to 1.

[thop]

we use 0.3 with a line over the three, looking like:

_
3

[Umfriend]

OK, prove mathematically that
~_
0.9 = 1 (the ~ is there to align the _)

[GNEP]

   _
0.1 = 1/9
   _     & nbsp;_
0.9 = 0.1 * 9 = 9/9 = 1

[Umfriend]

Oops, that one is simpeler than mine and can't be refuted (mine could, at least in words) AFAICS. Congrats......
Umf (sulking that it is even simpler than I thought for over 17 years...... )

[GNEP]

Can anyone remember that old "proof" that one of my maths teachers used to use that showed 63=64 or something??? That was amusing.

[Umfriend]

No, but I'd love to get to know that one...
Umf

[SitFlyer]

This seems interesting:

Theorem : All positive integers are equal.
Proof :
Sufficient to show that for any two positive integers, A and B, A = B.
Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction.
If N = 1, then A and B, being positive integers, must both be 1. So A = B.
Assume that the theorem is true for some value k. Take A and B
with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
(A-1) = (B-1). Consequently, A = B.

[GNEP]

Found something similar to what I was looking for:

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

Spot the flaw

[Umfriend]

Sitflier, assume N=2 and you will find that at least one of A and B equals 2, but not necessarily both.

GNEP, from line four to line 5, u r dividing by zero.... (right?)

Imf

[GNEP]

Umf - yup. a=b therefore a-b=0.

[SitFlyer]

Given
there is a camel
there are 3000 bananas at point A.
you want to get them to point B.
The distance between point A and point B is 1000 miles.
The camel can only carry 1000 bananas at a time,
and the camel eats 1 banana every mile.

The question is how many is the Maximum Bananas can you get to point B via the Camel.