How do you interpret algebraic expressions in terms of their context?

Question

Nathan Axel · Accepted Answer

A few examples...

I wonder about the context of this question, but here are a few ideas as to the sort of thing to which you might be referring... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In integer arithmetic: #7 -: 3 = 2" "# with remainder #1# In rational arithmetic: #7 -: 3 = 7/3# ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In real arithmetic: #root(3)(-1) = -1# In complex arithmetic: #root(3)(-1) = 1/2+sqrt(3)/2i# ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In integer arithmetic: #2# is a prime number In Gaussian integer arithmetic: #2 = (1-i)(1+i)# is a composite number ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In rational arithmetic: #x^2-x-1# is not factorable. In real arithmetic: #x^2-x-1 = (x-1/2+sqrt(5)/2)(x-1/2-sqrt(5)/2)# is factorable. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In real arithmetic: #x^2+x+1 = 0# has no roots. In complex arithmetic: #x^2+x+1 = 0# has two roots. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In real arithmetic: #x^3+x+1# is a one to one function. In complex arithmetic: #x^3+x+1# is a many to one function. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ In integer arithmetic any integer is odd or even but not both. In modulo arithmetic with an odd modulus (e.g. modulo #7# arithmetic), every number is both odd and even. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~