∀a ∈ℤ^+, ∃b,c∈Q such that bc≠0 and a^2=b^2+c^2 a. write the statement informally b. for a=1 and a=2 find rational numbers b and c such that bc≠0 and a^2=b^2+c^2 holds. explain. c. prove the statement stated in part a.

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.