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if the tip of the leaf is broken off will that leaf continue to grow?

I read it won't because the tip of the leaf produces a growth hormone for the leaf to grow.

No, it won't. They're monocots. They will grow new leaves from the stolons but the individual cut leaves will not regenerate and form a new growth point on that leaf. The same thing is true for other monocots, like grasses.

Correct - but, unlike grasses, you can propagate them by leaf cuttings. The cuttings will not be variegated, though, even if the mother plant was variegated - to get a variegated cutting you need a piece of the stolon from a variegated plant.

thanks

Yes, they should grow fine.