Let A, B be the ordered sets in Figure 10.3. Let C be the direct product of infinitely many copies of the two element chain 2. Then A^C is isomorphic to B^C, but A is not isomorphic to B.

The fact that different structures can be shown to be functionally isomorphic implies that they are analogous, not homologous.

For example, in so far as written and spoken English are isomorphic (i.e. have the same structure), they are the same language: there is nothing but their structure that they have in common.

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