Take for example this mundane thought experiment. It can also be done physically if you want!
Drop a ping pong ball and count its bouncing rate per second until it rolls. That's when it has transcended the definition of bouncing!
One would argue that you can't count its bounces when it's not bouncing. But if bouncing was a philosophically sound idea, it would have to apply universally. This is because discretion is a contrived way to understand the universe; only a holistic approach is philosophically precise.
What is the rate of bouncing of the ping pong ball once it rolls? What you find is that it's fair to decide any of the following:
• the ball is not bouncing per each unit of time (0)
• a roll is a single bounce (1) per each instant (if this is your unit of time) such that the ball has no time to really bounce since instants don't last
• the ball is bouncing at an infinite rate (per whatever unit of time) since there is only an instant between each bounce (∞)
These explanations are philosophically equivalent simply because they're each as fair as one another. You can't say that one is correct, and another isn't. Fundamentally, this is because the meaning behind each of the indiscrete numbers' symbols is equivalent.
This isn't to imply that this set of explanations is perfectly philosophically precise; rather, it exposes the contrivance of bouncing by demonstrating its eventual ambiguity. It gets us closer to a purely philosophical understanding. The set of explanations is still contrived to the extent that it is expressed using an inherently discrete language; the contrive of discretion remains, for it is necessary to use lesser contrives to unlearn greater ones.
These explanations are somewhat more real than other more discrete explanations you would have to describe nonextreme cases. Saying the ping pong ball is bouncing at a rate of 100 bounces per minute is inherently more discrete and approximate than describing the ping pong ball to be bouncing infinitely when rolling. This is because the description of infinity is absolute, nonrelative, meaning it can't be approximate and discrete since relativity is necessary for discretion and absoluteness is inherently not approximating.
This is a main insight of the equivalencies, the realization that ideas such as language contrive our understanding of reality. While useful in speech, pointing out a ball's bounces is not philosophically precise. Only something else, like recognition of a waveform, continuously part of a greater fractal wave of the universe, would be continuous with reality and thus philosophically precise.