Increasig Triplet Subsequence

/*
Logic:
IF we get a number less than or equal to i then update i.
if element is greater than i but less than equal to j,then update j.
and if less than j also then we have k also so return k.

try to deny this algo:
first we get 2 then 4 so i=2 and j=4
then again we get 1 so i=1 and j=4 now we get 6 so now k=6 and
we got the triplet. so it works in all case.
ie. 2,4,1,6
*/

class Solution:
    def increasingTriplet(self, nums: List[int]) -> bool:
        first=math.inf
        second=math.inf
        third=math.inf
        for i in nums:
            if i<=first:
                first=i
            elif i<=second:
                second=i
            else:
                return True
        return False