The discussion revolves around a function defined from a non-empty set X to its power set, specifically examining the subset Yf, which consists of elements in X that are not included in their corresponding f(x) values. Participants are tasked with determining Yf based on the function's definition.
The discussion is active, with participants engaging in back-and-forth questioning to clarify their understanding of Yf and its relationship to the function f. Some participants suggest that Yf includes all elements of X except the one being evaluated, while others seek to confirm their interpretations through examples.
Participants are working under the assumption that the function f takes an element n from set X and returns the set of all elements in X excluding n. There is some confusion regarding the definitions and implications of Yf, leading to a need for clarification on the relationship between elements and their corresponding f values.
hocuspocus102 said:f(1) in that case would be {2,3} right? but how does that translate to Yf?
hocuspocus102 said:no, so is Yf just X/x ?
hocuspocus102 said:no 1 isn't in it because it's x in X such that x not in f(x) and 1 is not in f(1)
hocuspocus102 said:I get that for f(1), 2 is in Y_f and 3 is in Y_f but 1 is not.
for f(2), 1 is in Y_f and 3 is in Y_f but 2 is not.
so for f(n) on a set of size t Y_f will have all numbers in the set 1 through t not including n in it. is that how you'd say that or is there a more explicit formula?
hocuspocus102 said:I don't know I thought f just took n to a set with all elements of X not including n because Y_f is x not in f(x)
hocuspocus102 said:no it's not
hocuspocus102 said:ohhhh. ok so Y_f is whatever value you plug in for x?
hocuspocus102 said:{1,2,3} are in Y_f because f(1) implies 1 is in it, f(2) implies 2 is in it and f(3) implies 3 is in it right?
hocuspocus102 said:it should
hocuspocus102 said:so Y_f is just X?
hocuspocus102 said:that's what I think