Originally posted by smw6869You use the euclidian division algorithm whenever you divide 'by hand'. Try to divide 1/3 using pencil and paper you see that you go into a repetition quite instantly, and you realize that you can fill in the threes as long as you like.
Dear Fabian, I have never experienced the euclidial division algorithm position. How many repititions? Over and over again? For how long? Gracious sakes, i must change my diapers. Later, king of the 50's rock and roll era.
Granny.
Those of you who don't know the euclidian division algorithm - google it.
Originally posted by FabianFnasI should have used Fabian's argument at Uni .. life would have been so much easier!
Using the euclidian division algoritm, as you do when you divide manually without any calculator, it is easily seen that the proof is unneccesary. Prform the algoritm and you'll see by yourself.
"... it is easily seen that the proof is unneccesary."
Originally posted by FabianFnasOh Fabian darling, i shall try the algorithm "by hand", but only till i get the repetitions down correctly then i hope you will show me the more advanced form, in person maybe. Just thinking of those Rock & Roll hands of yours makes me .......oops.
You use the euclidian division algorithm whenever you divide 'by hand'. Try to divide 1/3 using pencil and paper you see that you go into a repetition quite instantly, and you realize that you can fill in the threes as long as you like.
Those of you who don't know the euclidian division algorithm - google it.
Granny.
Originally posted by AThousandYoungbut is it? theoretically it goes on infinitely so why can't i do that?
You snuck in an extra +1 in the fourth step without including it's partner -1. This is incorrect.
If you had an infinite series you could stop after any term. so technically I haven't done anything wrong.
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Originally posted by ArachnarchistThe ... implies that the pattern repeats. The pattern with more +1's than -1's is different than the pattern with equal amounts of both.
but is it? theoretically it goes on infinitely so why can't i do that?
If you had an infinite series you could stop after any term. so technically I haven't done anything wrong.
The decimal definition of pi cannot be stopped after any term. Isn't it an infinite series?
Originally posted by ArachnarchistThis is not a proof, as we all know already.
how about this to prove 1=0
0= 0 + 0 + 0 + . . .
0= (1 - 1) + (1 - 1) + (1 - 1) + . . .
0= 1 - 1 + 1 - 1 + 1 - 1 + . . .
0= 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + . . .
0= 1 + 0 + 0 + 0 + . . .= 1
First - what does ... means? It means that there is a repetition of a pattern infinit number of times. It doesn't have an end.
So when I see the expression of 1-1+1-1+... I see this as a limit with n numbers of term and n approaching infinity.
Does this limit has a value? No, of course not. There are no last term. Using this expression as if it has a value you can easily "prove" that 1=0.
Originally posted by wolfgang59the reason that numbers and mathematical proof is vigour is because they go on infinitely. this is why we use numbers as time because they can be easily repeated and will continue on no matter what. if you can give me the highest number in the world known, ill gladly take it and add 1 to make it bigger.
How do you know its repeated forever?
The whole point of mathematical proof is its VIGOUR!
Aniways id like to move on to pi. does anybody know any puzzles that include pi? i like pie.
Originally posted by tournymangrMy favourite is
the reason that numbers and mathematical proof is vigour is because they go on infinitely. this is why we use numbers as time because they can be easily repeated and will continue on no matter what. if you can give me the highest number in the world known, ill gladly take it and add 1 to make it bigger.
Aniways id like to move on to pi. does anybody know any puzzles that include pi? i like pie.
http://www.redhotpawn.com/board/showthread.php?threadid=72379
Originally posted by FabianFnasAh, excellent point.
This is not a proof, as we all know already.
First - what does ... means? It means that there is a repetition of a pattern infinit number of times. It doesn't have an end.
So when I see the expression of 1-1+1-1+... I see this as a limit with n numbers of term and n approaching infinity.
Does this limit has a value? No, of course not. There are no last term. Using this expression as if it has a value you can easily "prove" that 1=0.