Problem 3 Countable and Uncountable Sets
(a) Show that there are uncountably infinite many real numbers...
Problem 3 Countable and Uncountable Sets
(a) Show that there are uncountably infinite many real numbers
in the interval (0, 1). (Hint: Prove this by contradiction.
Specifically, (i) assume that there are countably infinite real
numbers in (0, 1) and denote them as x1, x2, x3, · · · ; (ii)
express each real number x1 between 0 and 1 in decimal expansion;
(iii) construct a number y whose digits are either 1 or 2. Can you
find a way...
I cannot figure out how to get the ordered pair for x numbers 2,
3, 11,...
I cannot figure out how to get the ordered pair for x numbers 2,
3, 11, and 18 for square root f(x)= x - 2, for graphing.
How many valid 3 digit numbers can you make using the
digits 0, 1, 2 and...
How many valid 3 digit numbers can you make using the
digits 0, 1, 2 and 3 without
repeating the digits? How about with repeating?
5. These sets of quantum numbers are each supposed to specify an
orbital. One set, however,...
5. These sets of quantum numbers are each supposed to specify an
orbital. One set, however, is erroneous. Which one and why?
a. n = 3; l = 0; ml = 0
b. n = 2; l = 1; ml = –1
c. n = 1; l = 0; ml = 0
d. n = 4; l = 1; ml = –2
1. Consider sets AA and BB with |A|=9|| and |B|=19..
How many functions f:A→B are there?...
1. Consider sets AA and BB with |A|=9|| and |B|=19..
How many functions f:A→B are there?
Note: Leave your answer in exponential form. (Ex: 5^7)
2. Consider functions f:{1,2,3}→{1,2,3,4,5,6}.
How many functions between this domain and codomain are
injective?
3. A combination lock consists of a dial with 39 numbers on it.
To open the lock, you turn the dial to the right until you reach
the first number, then to the left until you get to the second
number,...
how
many odd numbers can be formed from the digits 0,1,2,3,4,5,6 if
each digit can be...
how
many odd numbers can be formed from the digits 0,1,2,3,4,5,6 if
each digit can be used only once?
Part A Identify which sets of quantum numbers are valid for an
electron. Each set is...
Part A Identify which sets of quantum numbers are valid for an
electron. Each set is ordered (n,ℓ,mℓ,ms). Check all that apply.
3,1,1,-1/2 1,1,0,1/2 3,3,1,1/2 3,3,-2,-1/2 4,3,3,-1/2 2,1,-1,-1/2
0,2,1,1/2 4,3,4,-1/2 3,2,-1,-1/2 3,2,1,1 3,1,-1,1/2
3,-2,-2,-1/2
MATLAB
Task: Use a for loop to find
how many numbers you have to add to...
MATLAB
Task: Use a for loop to find
how many numbers you have to add to get a sum greater than 1,000.
The numbers in the problem are consecutive, so adding up
1+2+3+4+5+6+.... until you reach the user defined value 1000.
Method : must Make a variable equal to 1 then
add 2, 3, 4...to it, until you reach 1000, then you break out the
loop once the sum hits 1,000.