The simplest example of continuity is time. Time is never ending (well, you could argue it began with the Big Bang, but let’s not argue the minutiae!). If you try and count from the beginning of time until the end of time, well… you can’t. It’s also continuous if you zoom in to a particular point (or try to). Let’s say is takes you 20 seconds to run 100m. It’s probably not precisely 20 seconds; More likely it’s 20.01 seconds, 20.001 seconds, or even 20.00000001 seconds. The most accurate measuring device we have for time is the atomic clock, swimming at 500 trillion times per second and reports time with 19 decimal places. But that doesn’t mean time only exists in 19 decimal place increments; It’s just the best we can measure—for now.
