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I would argue that this formulation is outright confusing not because it is so dense but because it has so much unnecessary cruft to misguide the reader. The e
by j-pb 10y ago
I would argue that this formulation is outright confusing not because it is so dense but because it has so much unnecessary cruft to misguide the reader.
The entire formula of
{f ∈ [1..N ⟶ 1..N] : ∀ y ∈ 1..N : ∃ x ∈ 1..N : f[x]=y}
could actually be written as
[1..N ⟶ 1..N]
Most CS people myself included will not trust their own senses when confronted with such a tautological statement and continue to search for meaning where there is non because it is so common to encounter cases in your everyday code where something that you thought was dead code has actually semantic meaning.
- berbc 10y agoIf by [1..N ⟶ 1..N] you mean the set of functions from [1..N] that have values in [1..N], I think you are wrong. The formula in the post describes a subset, the set of such functions that are surjective.
- deleted 10y ago[deleted]
- j-pb 10y agoYeah I think your right, in this context I saw the case of [ A -> B ] as a function from coimage A to image B which are all bijective. But it is meant as the more standard domain A to codomain B. His natural language description is somewhat lacking in that aspect > I had already explained that [1..N ⟶ 1..N] is the set of functions that map the set 1..N of integers from 1 through N into itself,
- sampo 10y agoWell, he did say "into itself", not "onto itself".