







Is this operation associative? 
20140114 

patrick pose la question : 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!! Penny Nom lui répond. 





A binary equation 
20090707 

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





An associative binary operation 
20080908 

Skye pose la question : 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! Harley Weston lui répond. 





Is this operation associative? 
20080906 

Francesca pose la question : 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. Penny Nom and Victoria West lui répond. 





Binary words 
20070909 

Jan pose la question : 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. Penny Nom lui répond. 





A binary operation 
20070731 

sofia pose la question : 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. Penny Nom lui répond. 





Binary operations 
20070730 

jim pose la question : prove or disprove:
Every binary operation on a set consisting of a single element is both commutative and associative.
Penny Nom lui répond. 





10^100 in binary form 
20060510 

Headmaster pose la question : How many digits has the number 10^{100} if we write it in binary form? Chris Fisher, Paul Betts and Steve La Rocque lui répond. 





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

Leandro pose la question :
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Chris Fisher and Penny Nom lui répond. 





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

Bill pose la question : 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? Harley Weston lui répond. 





Paying with silver 
20000426 

Luther Jackson pose la question : 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. . . . Claude Tardif and Penny Nom lui répond. 





Bases other than 10 
19991206 

Garret Magin pose la question : 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. Claude Tardif and Patrick Maidorn lui répond. 

