Re:Finding a Bug in Dummit and Foote's Abstract Algebra
by changoplatanero on Monday September 07, 2026 @05:24PM
(#49603142)
When there are no pairs, its certainly true that the first element of each pair comes from A. Just like if there are no living dinosaurs its true that all living dinosaurs speak English.
Re:Finding a Bug in Dummit and Foote's Abstract Algebra
by psYchotic on Monday September 07, 2026 @05:43PM
(#49603280)
That helps. Thank you!
I was trying to come up with something to explain why I couldn't see it myself: every element of an empty set of integers is both even and odd. This feels counterintuitive to me, until I flip it around into a question: what is the set of all integers that are both even and odd?
The first criterion for a function is stated as:
> The first item in each pair comes from A.
The counter-evidence for the proposition says:
> Let A = {}, and B = {1}. Let f: A -> B = {}
How does this f satisfy the first criterion, if A is uninhabited? It feels like this function can't be invoked. Am I thinking too much in terms of types here?