User blog comment:MilkyWay90/Help with understanding Veblen array notation/@comment-30754445-20180811202716/@comment-31966679-20180819224128

Also, for rule 3, what did you mean x < c if c was a limit ordinal in the sup function (sup{φ(a, b, ..., x) with x < c})? You couldn't subtract c by 1, as it is a limit ordinal.

If you tended for x to go higher and higher and higher, it'd eventually reach c, and then it'd be equal to c!

For example if c was was epsilon-0:

i'd evaluate φ(a, b, ..., omega) first

then φ(a, b, ..., omega ^ 2) second

φ(a, b, ..., omega ^ omega)

φ(a, b, ..., omega ^^ 2)

then omega ^^ 3

then ^^ 4

and so on...

So what did you mean by x < c?