  In this article we address the problem of automatic answer checking in
interactive learning systems that support mathematical notation. This problem
consists of the problem of establishing identities in formal mathematical
systems and hence is formally unsolvable. However, there is a way to cope with
the issue. We suggest to reinforce the standard algorithm for function
comparison with an additional pointwise checking procedure. An error might
appear in this case. The article provides a detailed analysis of the
probability of this error. It appears that the error probability is extremely
low in most common cases. Generally speaking, this means that such an
additional checking procedure can be quite successfully used in order to
support standard algorithms for functions comparison. The results, obtained in
this article, help avoiding some sudden effects of the identity problem, and
provide a way to estimate the reliability of answer checking procedure in
interactive learning systems.
