Minimum value selection

Question

Code

 y[1] = 1;
 y[2] = 2;
 y[3] = 3;
 Min[y[1], y[2], y[3]]

Outputs "1", but desired result is y[1]

How to do that? Many thanks for help.

Answer 1

You can get the value(s) i for which y[i] is minimal :

 y[1] = 10;
 y[2] = 20;
 y[3] = 30;
 MinimalBy[Range[3],y]

{1}

But as soon as you wrap the result 1 in y[...], y[1] will be evaluated to 10, accordingly to the princips of Mathematica.

Answer 2

For the exact example given you could perhaps utilize the DownValues list:

MinimalBy[DownValues[y], Last][[1, 1]]

HoldPattern[y[1]]