Consider the quotient which can be identified to the circle . The irrationality of is equivalent to the injectivity of the quotient map restricted to . The claim serves to demonstrate that for each neighborhood that is open in there is always a with , i.e.
Think about the translations for (still open, of course). IIf you can locate an such that there exists then and you are done.
If not, it means that for all , . But this says that is discrete in and since is compact, this is in contradiction with its infinitness.
Find the volume V of the described solid S
A cap of a sphere with radius r and height h.
Whether each of these functions is a bijection from R to R.
In how many different orders can five runners finish a race if no ties are allowed???
State which of the following are linear functions?
Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?
A square is also a
D)none of these
What is the order of the numbers from least to greatest.
Write the numerical value of
Solve for y. 2y - 3 = 9
How to graph ?
How to graph using a table?
How to find the vertex of the parabola by completing the square ?
There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?
Write 18 thousand in scientific notation.