Fortunately, we know that there is a'natural'surjection-from the class of pairs of an even denominator with an odd nominator-on the class of even fractions which are received by the original definition; Thanks to this surjection, we can receive a unique definiendum of " " even fraction " ", by replacing the previous " indefinite " definition by a " definite " definition, which is received by deviding the original definition into sub-definitions, each of which defines " the " ( unique ) " even fraction " as " the " ( unique ) irreducible fraction whose " given " denominator is even and whose " given nominator is odd ", in such a way that this devision of the original definition into sub-definitions-succeeds to preserve the original class of " " even fractions " " received by the original " indefinite " definition.
12.
Ignoring the very issue of " " even fractions " " ( and fractions at all ), "'do you know of any ( well-known ) similar process, in any mathematical realm you are familiar with ? "'i . e ., a process in which the classical definition of Y ( whatever Y is ) does not yield a unique definiendum; however, thanks to the existence of a'natural'surjection ( whatever this'naturality'means )-from the class of X's-on the class of Y's received from the original definition, we can receive a unique Y, by replacing the previous " indefinite " definition by a " definite " definition, which is received by deviding the original definition into sub-definitions, each of which refers to a given X ( by which Y can be defined uniquely ), in such a way that this devision of the original definition into sub-definitions-succeeds to preserve the original class of Y's received by the original " indefinite " definition.
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