Hi i just start learning algebra.(adsbygoogle = window.adsbygoogle || []).push({});

Here are some definitions and examples given in Wikipedia:

1.Anisomorphismis a bijective map f such that both f and its inverse [itex]f^{-1}[/itex] arehomomorphisms, i.e., structure-preserving mappings.

2.A homomorphism is a structure-preserving map between twoalgebraic structures(such as groups, rings, or vector spaces).

3.Consider the logarithm function: For any fixed base b, the logarithm function [itex]\log_b[/itex] maps from the positive real numbers [itex]\mathbb{R^+}[/itex] onto the real numbers [itex]\mathbb{R}[/itex]; formally:[itex]\log_{b}:\mathbb{R^+}\rightarrow\mathbb{R}[/itex]

This mapping is one-to-one and onto, that is, it is a bijection from the domain to the codomain of the logarithm function. This is an isomorphism on set.

Question(not h.w.):Setis not an algebraic structure as no operation is defined in it. From(1), isomorphism is also homoporhism.

From(2), there is no homoporhism on set.

So why is there isomorphism on set?

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# Simple question about isomorphism

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