







Is this operation associative? 
20140114 

From patrick: Associative test: Can you explain the following to me?
Is the following operation associative?: x*y=x+y+1
1) x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2
2) (x*y)*z=(x+y+1)*z=(x+y+1)+z+1=x+y+z+2
The answer is yes as 1) = 2)
My specific questions are:
1) How x*(y*z)=x*(y+z+1)=x+(y+z+1)+1 ?
2) How (x+y+1)*z=(x+y+1)+z+1?
Thank you!! Answered by Penny Nom. 





A binary equation 
20090707 

From Chinonyerem: Find a bitwise solution (i.e find xi so that each xi E {0,1}) to
32 = x1 + 2x2 + 4x3 + 9x3 + 20x5 Answered by Harley Weston. 





An associative binary operation 
20080908 

From Skye: Suppose that * is an associative binary operation on a set S. Show that the set H={a E S such that a*x=x*a for all x E S} is closed under *. (We think of H as consisting of all elements of S that commute with every element in S.)
Thanks! Answered by Harley Weston. 





Is this operation associative? 
20080906 

From Francesca: Determine whether the binary operation * defined is commutative and whether * is associative
* defined on Z by a*b = ab\
I understand how to figure out if it's commutative, but I thought for a binary operation to be associative, it had to have at least three elements, so I don't know how to tell if this associative or not. Answered by Penny Nom and Victoria West. 





Binary words 
20070909 

From Jan: A computer word is made of strings of 0's and 1's. How many different words can be formed using 8 characters?
Example is 01010101. Answered by Penny Nom. 





A binary operation 
20070731 

From sofia: Prove that if * is associative and commutative binary operation on a set S, then
(a*b)*(c*d) = [(d*c)*a]*b
for all a,b,c,d element in S. Assume the associative Law only for triples as in the definition that is, assume only
(x*y)*z = x*(y*z)
for all x,y,z element in S. Answered by Penny Nom. 





Binary operations 
20070730 

From jim: prove or disprove:
Every binary operation on a set consisting of a single element is both commutative and associative.
Answered by Penny Nom. 





10^100 in binary form 
20060510 

From Headmaster: How many digits has the number 10^{100} if we write it in binary form? Answered by Chris Fisher, Paul Betts and Steve La Rocque. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





x^{ 4} + x^{ 5} = 100 
20021027 

From Bill: One of my students has stumped me. He asked how to solve the equation 4^{ x} + 5^{ x} = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston. 





Paying with silver 
20000426 

From Luther Jackson: A silver prospector is unable to pay his March rent in advance. He owned a bar of pure silver, 31 inches long, so he made the following arrangement with his landlady. He would cut the bar, he said into smaller pieces. On the first day of March he would give her and inch of the bar, and on each succeeding day he would add another inch to her amount of silver. She would keep this silver as security. At the end of the month, when the prospector expected to be able to pay his rent in full, she would return the pieces to him. . . . Answered by Claude Tardif and Penny Nom. 





Bases other than 10 
19991206 

From Garret Magin: We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know. Answered by Claude Tardif and Patrick Maidorn. 

