Need Smart Person (math question)

There is another place.

Consider the circle one mile in circumfrence, centered on the South Pole.
Start from a point one mile North of that circle.
Go one mile south (and you are now on that circle)
Go one mile east (you've walked around the South Pole)
Go one mile north and you are at your starting point.

For the mathematicaly insane of us, the circles of circumfrence 1/n miles (n integer) determine a family of solutions to this puzzle.

 

Congratulations, Mike!
You have just won an all expenses paid five year vacation at Vostok Station, Antarctica. For those who don't know, Vostok is widely rated as the coldest place on Earth -- even colder than Winnipeg in January.

You will receive your ticket in the mail shortly. Return ticket will be dated 28 May, 2012, courtesy of Aeroflot. If they're still in business five years from now.

 

Cool! Very cool!

 

Darn. >.< Thought I was right.

 

Thats not a bad little puzzle, I may set it as a question some time. Still struggling to see what it has to do with planes though.

 

In all cases, you need a plane to get to the starting point.

 

No. 0.999=0.999, 0.9999999999=0.9999999999, 1= 1. Why not just say that 5000 = 1? If you round to the nearest then you have to present any results with the appropriate uncertainty. You can't add an uncertainty and then pretend it doesnt exist, otherwise why bother counting in the first place.

 

By the ellipsis (three dots), Nacht is referring to the limit of a sequence, namely the infinite series

.999... = SUM (K=1 TO INFINITY) 9 x 10 ** (-K)

where ** denotes exponentiation.

(Let me know if you know how to post math symbols on this site, or even Greek letters.)

The limit of this sequence is in fact 1.

 

No matter how many 9's there are it isn't equal to 1. The = symbol represents something being equal to another. For the instance of a limit there is the 'lim', symbol. For example a limit can be ambiguous, lim 1/x x->0 is ambiguous, no equality can be determined here at least not without determining the direction the limit is taken. I appreciate that for all intense and purposes they are same and infact calculus relies on the power of limits. But there are few things in maths I find quite as annoying as proofs that 1.1 = 1 = 3 = 5 = 100000, clearly if this is true then I am a millionaire or more likely the '=' is being misused by definition.

 

lim 1/x x-> 0 does not exist. It is easy to demonstrate than given any positive real number M, there is a value x such that (1/x) > M, with a corollary (1/(-x)) < - M.

If you have seen a proof that 1.1 = 1 = 3, et cetera, please share it with us.

There is nothing ambiguous about the limit of a real-valued function of a single real variable. For any value of the domain, the limit does or does not exist.

As for lim n -> infinity sum (k=1 to k=n) [9 X 10**(-k)] = 1,
this is equivalent to saying than given any real number b > 0, there is a value M > 0
such that
n > M ==> abs {1 - sum (k=1 to k=n) [9 X 10**(-k)] } < b.
That is another way of saying that an infinite series, which is the limit of a sequence of sums, is convergent.

 

http://en.wikipedia.org/wiki/Invalid_proof

 

Nice page, do they have one for statistics abuse?

 

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"(1) Peter Rabbit showed up at the Infinity Hotel one evening, but the clerk said it was full. Peter said the clerk could make room if he was willing to rearrange the guests. But how?
(2) Peter was impressed by the service, so the next night he came back with an infinite number of friends, but once again the hotel was full. How could the clerk accommodate all these new guests by rearranging room assignments?
"


Regarding the Peter rabbit question 2 it would not mater they would collapse into a black whole with that many friends and as they say a black whole has no hare.

 

oh god is this the .9 repeating equals one thread? they're a dime a dozen. I'm not a mathematician, but here's my take.

(1/3)=.3 repeating
?=.9 repeating
(.9 repeating)/(.3 repeating)=3/3=1

 

my bad, I skipped towards the end and was under the impression this has something to do with that. my bad, I thought wrong. sorry about that.

 

Of course, there are many one-to-one mappings of the natural numbers onto other sets. For example,
f(n) = n + 1
g(n) = 2n
h(n) = 2n + 1.
In the case of Peter Rabbit, the clerk first empties the hotel. Then he puts the new guest into room 1. Each guest previously there in room n is now put into room n + 1.
When Rabbit shows up with an infinite number of friends, the clerk again empties the hotel. He then puts the previous guests into the even numbered rooms and the new guests into the odd numbered rooms.

 

to make the proof even more simple that way your 5th grade brother can understand it, get him to understand that if you subtract two things and the difference is z, then they are the same number. Having said that, subtract .999(repeating) from 1. Show hi that in 1, the .000 repeats, and then try to carry over...