You can use the -textFieldDidEndEditing: method from the UITextFieldDelegate protocol. This method is called whenever a text field resigns the first responder status (i.e. Ends editing).
This is the chance to check the entered String. If you want to perform a check after each character that has been input, use -textField:shouldChangeCharactersInRange:replacementString: as donkim suggests.
For the textfield, you could use the UITextFieldDelegate and implement the textField:shouldChangeCharactersInRange:replacementString: method. According to the docs, "the text field calls this method whenever the user types a new character in the text field or deletes an existing character." In the method, you should do a check for all non-number characters and remove them.
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