1. (a) For an arbitrary set Y , determine

(b) For an arbitrary set X, determine

(a) I couldn't figure it out

(b) I think it's the empty set but I can't show how

if anyone could show me how I would greatly appreciate it

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- October 14th 2008, 09:27 PMjbpellerina little bit of functions on sets
1. (a) For an arbitrary set Y , determine

(b) For an arbitrary set X, determine

(a) I couldn't figure it out

(b) I think it's the empty set but I can't show how

if anyone could show me how I would greatly appreciate it - October 15th 2008, 04:33 PMJhevon
- October 15th 2008, 05:08 PMPlato
We can find disagreement on this question.

Paul Halmos claims the following.

“(i) has exactly one element, namely , whether is empty or not and (ii) if , then ". - October 15th 2008, 05:31 PMJhevon
is my interpretation of the problem correct? in other words, is Halmos saying the set of function from the empty set to another set is empty, and thus, represented by the empty set?

it seems strange that we should require X is nonempty in part (ii), since that is just a special case of part (i) (where Y is empty).

how exactly is this claim justified? what are the other interpretations? - October 15th 2008, 05:49 PMPlato
- October 15th 2008, 06:13 PMJhevon
- October 15th 2008, 07:06 PMPlato
Well I must say that my experience is different from the vast majority on mathematicians. In all my graduate training, my professors did not believe that a set could be empty. How can a point set be empty? If it is a point set then by definition it is not empty. Of course, that is a very narrow and not practical position.

For me a function is a set of ordered pairs: .

I am not sure what mean.

In many ways, this is a pointless question.