The periodic table is set to get a new addition say hello to the superheavy element ununseptium
There are 60 seconds in a minute. There are 60 minutes in an hour. And a day has twenty-four hours 12 hours of daylight and 12 hours night averaged through the year.
What makes the numbers 12 and 60 so special?
Please Tell me how I can show
We must prove that bothand . is clear since is a subset of .
To prove the other inclusion, supposeand let . . If we are done. If then, since , we have as well. In either case . Hence .
The best site to visit if youre interested in IMO, IMHO, is this one: http://www.artofproblemsolving.com/
Their forum: http://www.artofproblemsolving.com/Forum/index.php?
Lets assumeis 1 or prime. Then it divides 2 or .
(i)divides 2 or or . So .
(ii)divides . For this to be an integer, . So . So which is the same as (i) above.
Soif is 1 or prime. There are other solutions if is not 1 and not prime but as you are not told to find them all, I think Ill stop here.
Contradictory is perhaps not a good word to use in the title of this thread. Oxymoronic might be better, I believe. It is not contradiction that I wish to explore, but rather oxymoron: http://z8.invisionfree.com/DYK/index.php?showtopic=69
If I said that someone was an unpleasant kind of person, I would be uttering an oxymoron.