Bobic said:
There's no such thing as an unstoppable force or an immovable object so the question is kinda redundant
But for the sake of argument
F=ma
unstoppable force - F = infinity
immovable object - m = infinity
infinity = infinity*a
a=infinity/infinity
a=1
(i'm aware this is mathematically daft but it's too late for me to care)
Sorry, but my physicist/math suspenders popped on this one, and I want to clarify people's understanding of the mathematics before they run around screaming stuff that isn't correct.
This statement is not actually correct. Infinity/Infinity is an indeterminate quantity because the actual answer can be anything. The specific answer for any given situation must be obtained by applying a limit process by which the numerator and denominator simultaneously tend toward infinity so that algebraic cancellations allow the specific value of the ration F/m to be obtained. However, to do this, you need the formulaic forms of F and m depending on some common parameter such there is a particular value of this parameter which simultaneously causes F and m to be infinite. Then you can use algebraic cancellation of terms between the numerator and denominator to arrive at the limit answer as the independent parameter tends toward the specific value causing F and m to simultaneously tend toward infinity. So you would have something like this:
Make F and m be monotonically increasing functions of a parameter lambda such F and m simultaneously tend toward infinity as lambda tends toward a specific value c
F = F(lamba)->INF as lambda->c
m = m(lamba)->INF as lambda->c
Then we find the acceleration a through the limit process as lambda->c
limit[F(lamba)/m(lamba), lambda->c] = a
The specific value obtained for a will depend on the functional forms of F and m as monotonic functions of lambda. The simultaneity is key to obtaining a finite value. If F tended toward infinity faster than does m, then the limit process would produce that the acceleration a is, in fact, infinity. If m tended toward infinity faster than does F, then the limit process would produce that the acceleration m is, in fact, zero. Only in the case that they both tend to infinity at the exact same rate as they near infinity do we have the possibility of obtaining a finite, non-zero acceleration. So, what happens when an irresistible force(F = INF) meets an unmovable object(m = INF)? The answer is it depends on how you obtained the force and the object.
Other indeterminate forms are things like INF*0, 0^0(no, this doesn't equal 1; you can't do this), INF - INF, 0/0(this one is quite common), 1^INF. The reason these are indeterminate is not that one cannot find an answer; it's that there is no singular value that is always the answer. It depends on the functions leading to the indeterminate form.