It is important not to confuse the description with that which is described: even the most abstract-looking description of a mathematical structure is still not the structure itself. Rather, the structure corresponds to the class of all equivalent descriptions of it. Table 10.2 summarizes the relations between these and other key concepts linked to the mathematical-universe idea. Figure 10.7: Three equivalent descriptions of the same mathematical structure, which mathematicians would call an “ordered graph with four elements.” Each description contains some arbitrary baggage, but the structure
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