Fallacy of the Slippery Slope

Abuse of continuity

The slippery slope fallacy is committed by arguing that there is no difference between two situations since you can gradually get from one to the other through a long series of small changes or without a perceived abrupt break or discontinuity. -

example:

If A is accepted, then B must be accepted, which is just different from A If B is accepted, then C must be accepted, which is just different from B If C is accepted, then D must be accepted, which is just different from C … If X is accepted, then Y must be accepted, which is just different from X If Y is accepted, then Z must be accepted, which is just different from Y

But Z is unacceptable, so A should not be admitted