Sampling theory is aimed at providing a mathematical justification for inferences to some population value on the basis of knowledge of a subset, or sample, of that population.

Thus the vaccination programme will raise the average age of infection, another mathematical justification for a result that might have been intuitively obvious.

The field *R includes, in particular, infinitesimal ("infinitely small") numbers, providing a rigorous mathematical justification for their use.

Interestingly, the much-derided use of coincidence to further a plot has some mathematical justification.

Problem: assuming that time-reversal is possible, create a mathematical justification for conversion from matter to anti-matter to matter again before the completion of a journey.

As already mentioned above, the mathematical justification for this latest extension was delayed by three centuries.

This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field.

What if Mallansohn had stumbled on the Temporal Field without being aware of the mathematical justification?

There was some mathematical justification for the concept, and it certainly tidied up things, but soon other scientists exposed weaknesses in the equations.

The mathematical justification for the method is from the following longer mathematical procedure.