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Advanced Math/Abstrakt algebra
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Question
Hello,
I begin study abstrakt algebra and want to ask you :
Let S be aset having exactly one element.
How many different binary operations can be defined in S? Answer the question if S has exactly 2 elements, exactly 3 elements, exactly n elements.
Thank you very mach.
Hello Tetyana,
For 1-element, there are 2^(1*1)=2
For 2-elements, there are 2^(2*2)=16
For 3-elements, there are 2^(3*3)=512
For n-elements, there are 2^(n*n)=2^(n^2)
Check the following site for the details:
http://logic.stanford.edu/classes/cs157/2005/problems/backgroundsol.txt - a bit past the middle of the page.
Abe
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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