document.write( "Question 916124: Determine whether the function f : Z × Z → Z is onto if
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\n" ); document.write( "I know that \"is f onto\" is equivalent to \"Given any integer k, can you find two integers m and n such that [insert function value here] = k?\"
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\n" ); document.write( "Wouldn't that make ALL of them onto? If not, why not? \n" ); document.write( "
Algebra.Com's Answer #555950 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
No.  Not (b) since absolute values are never negative!\r\n" );
document.write( "Let's go through them:\r\n" );
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document.write( "(a) is onto because for any k ∈ Z, f(k,n) = k, for any n ∈ Z\r\n" );
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document.write( "(b) is not onto because for any k ∈ Z where k < 0, \r\n" );
document.write( "    f(m,n) = |n| ≠ k for all m,n ∈ Z\r\n" );
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document.write( "(c) is onto because for any k ∈ Z, f(k+1,1) = (k+1)-1 = k\r\n" );
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document.write( "Edwin
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