In floating-point arithmetic, this means that a number would be followed by an infinite number of trailing zeroes if there were enough bits.

Often an operation will be specified as having an infinitely-precise n-bit rounded answer. This is a kinda funny way of saying the (finite) precision of the result is known. But for general algos, the term is applied for when an arbitrarily precise result can be found in bounded time.

So, infinitely precise is the CS term for completely perfect, but dem clever mathematicians mostly just redefine it to mean precise enough and not lyin'.

This node is infinitely precise after being rounded ±2^{-16} nodegel-bits.

The funky usage of this terminology prolly results from some FPU designers tiring of specifying their devices in terms of the real algebra they can't do, and moving to a more optimistic style of only talking about what they can do perfectly well.