Recent content by hello3719

Apparently it seems that a number is defined as being an element of some defined set. It is quite funny that "element" and "number" mean the same thing. So in fact we can define anything we want as a number !

Hint: translate the problem using a system of equations.

1st find the desired sample space ie: how many ways are there to have 3 heads in a row out of 64 tosses? don't rush to nCr and nPr just now, think about the possibilities. then find the total number of possibilities and use the definition a probability.

As of now i don't think there is any result linking both together but you can always try. good luck.

Wow, this clears things up, tx :smile:

how many beers did you take? This is quite ridiculous.

tx ok, so they are are mapped to themselves sorry my logical flaw was that i wanted inconsciously a mapping of every irrationnal number to a general number not described in function of itself

so those which are not changed are not "associated" to some real number ? sorry maybe I am skipping something obvious

How can we be sure that every irrationnal number is of the form q + (n+1) \sqrt{2}

ok ill be more clear, Could you find a way to map EVERY irrationnal number to some real number or the other way around. Sorry but hadn't took any analysis courses yet, so I don't know the terminology well.

I guess you won't be able to determine a specific bijection between the irrationnal and real numbers. Maybe because the irrationnal numbers are uniquely defined as numbers which are "not rationnal numbers", only defined as what it is not.

yes it can be mapped on itself, but what is the use to do that, prior to the definition of a cardinal number. il let hurkyl prove you post#39, since I am not a loyal supporter of our "new"(post-cantorian) version of set theory. when i get the definitions straight i might get into those things.

Sorry to interrupt, but what is a "cardinal number" other than the bogus definition which refers to : "Set A has the same cardinal number as set B if they can be put into 1to1 correpondance with each others" In every analysis book I've looked up this is the only definition which popups. You...

yea, it is all about quantity in this world today, who cares about quality!

:smile: That is the most weak theorem ever, i mean cmon the definitions used are so empty. I bet it isn't a mathematician who suggested that theorem. ( Maybe a physicist, they like to play with "large numbers" :-p )