Changes between Initial Version and Version 1 of Ticket #16820, comment 38


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Timestamp:
04/19/15 17:22:18 (7 years ago)
Author:
darij
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  • Ticket #16820, comment 38

    initial v1  
    1212> I would say the set of 0x0 matrices is the empty set, not the set containing a unique element, the empty matrix.
    1313
    14 There are very good reasons for considering it a one-element set. Matrices of size m \times n correspond to morphisms R^n \to R^m. How many morphisms are there from R^0 to R^0 (that is, from 0 to 0) ? One -- the zero morphism.
     14There are very good reasons for considering it a one-element set. Matrices of size m \times n correspond to morphisms `R^n \to R^m`. How many morphisms are there from `R^0` to `R^0` (that is, from 0 to 0) ? One -- the zero morphism.
    1515
    1616> As for the oddity, I think we need a better/more uniform system for equality for things that behave like 0. At the very least, this is an issue with `CombinatorialFreeModuleElement` that deserves a separate ticket: