Hey Tina
You are right that when it is fully cycled, the value will probably read 0, and should read 0.
But they are still present, if you dont believe me check with your local water supplier, they usually offer detailed analysis of the tap water in your area. You will find that all three are present, although in very small amounts.
Ammonia is a waste product which is created by the inhabitants/plants/food, any organic waste in the tank, when you cycle a tank, what is happening is that the bacterial population of the tank is building up in order to handle the waste products present in the water. And as such, new ammonia is being added with every piece of organic matter decaying in the tank, the only difference is that a cycled tank is able to cope with this, while an uncycled tank is not.
I am not proposing that they are not harmful in larger amounts, merely stating that it is always present in water with more or less any form of life. :happy:
I would also add that you can cycle a tank while you have inhabitants in it, as long as you carefully monitor the water and do nescessary water changes. While this is not optimal, it is sometimes the only option and it can be done without putting an Axolotl through too much stress.
Regards Bjorn