Mathematica Pattern matching and replace repeated

[6.28318531]

I decided to ask here as well, because maybe someone will see it. Given a list of integers, use pattern matching and //.to create a rule that generates an ordered list of integers that are larger than the previous numbers in the list, eg given {3,5,2,0,6,1,8,4,9}, you should get {3,5,6,8,9}.I tried something like rules = {x_,y_,__}/;x>y -> {x,___}, calling our list L, L//.rules . I haven't really used this function before, what is the correct syntax? I want to check pairs of numbers and discard one if its less than the other. Any help would be appreciated.

 

[djelovin]

Here is one version (without rules):

larger[lst_] := Select[Transpose[{lst, Prepend[Most[lst], lst[[1]] - 1]}], #[[1]] > #[[2]] &][[All, 1]]

e.g.

larger[{3, 5, 2, 0, 6, 1, 8, 4, 9}]

gives:

{3, 5, 6, 8, 9}

 

[6.28318531]

Okay thanks