Transfinite arithmetic --- Introduction ---

This is an exercise as well as a game. Let a set E of k elements in the finite ring libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) ℤ/nℤ, represented by k integers between 0 and n−1. For any element libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) t∈ℤ/nℤ, the addition or multiplication by t transforms E into another set libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) E t⊂ℤ/nℤ.

Thus the exercise generates two sets E,libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) F⊂ℤ/nℤ, of the same number of elements, and asks you to transform E into F by successive additions and multiplications by elements of libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) ℤ/nℤ. And you will be scored according to the number of steps you make.

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