Repelling a very weak permanent magnet with an electromagnet

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I have a question about magnetic repulsion. Suppose I have a permanent magnet (axially magnetized) placed on top of the iron core of an electromagnet. I want to switch on the elctromagnet to repel the permanent magnet. (Please assume the permanent magnet is contained in some kind of tube that allows up and down movement but prevents it from spinning around. Please also assume that the electromagnet always produces a field strong enough to repel the permanent magnet - whatever that may be)
If the permanent magnet's magnetic field is very weak, will the electromagnet have trouble repelling it?
I know that if the electromagnet were attracting the permanent magnet, the only thing that would matter would be the strength of the electromagnet. What about repelling the permanent magnet? Assuming the electromagnet is always strong enough, does the magnetic field of the permanent magnet play any role? Is there a chance that an extremely weak magnet would simply act as a piece of ferrous metal and not be repelled by the electromagnet at all?
 

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