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## Main Question or Discussion Point

When we say that two algebraic expressions, [tex]f(x_1,x_2,\cdots x_n)[/tex], [tex]g(x_1,x_2,\cdots x_n)[/tex] are identical, or

[tex]f(x_1,x_2,\cdots x_n)\equiv g(x_1,x_2,\cdots x_n)[/tex], we mean (according to my textbook) that [tex]\forall x_1,x_2,\cdots x_n: f(x_1,x_2,\cdots x_n)=g(x_1,x_2,\cdots x_n)[/tex]

However, does that mean that

[tex]x^2+x\equiv0[/tex]

in [tex]Z^2[/tex]?

If not, does it mean that

[tex]f(x_1,x_2,\cdots x_n)\equiv g(x_1,x_2,\cdots x_n)\Leftrightarrow\forall\phi: \phi(f(x_1,x_2,\cdots x_n))=\phi(g(x_1,x_2,\cdots x_n))[/tex]

[tex]f(x_1,x_2,\cdots x_n)\equiv g(x_1,x_2,\cdots x_n)[/tex], we mean (according to my textbook) that [tex]\forall x_1,x_2,\cdots x_n: f(x_1,x_2,\cdots x_n)=g(x_1,x_2,\cdots x_n)[/tex]

However, does that mean that

[tex]x^2+x\equiv0[/tex]

in [tex]Z^2[/tex]?

If not, does it mean that

[tex]f(x_1,x_2,\cdots x_n)\equiv g(x_1,x_2,\cdots x_n)\Leftrightarrow\forall\phi: \phi(f(x_1,x_2,\cdots x_n))=\phi(g(x_1,x_2,\cdots x_n))[/tex]