What is continuity and discontinuity ?

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Can we move continuously, that is to say, gradually passing through all intermediate values, without skipping or breaking from inactivity to activity, for a neuron transmitting a jerk, for a particle emitting a photon of light for a ground plate starts to deflect to a company changing social bases, suggestive of a brain image, a living being growing up, for one species changing qualitatively, for example by "inventing" the birth in the egg or the spine or a radioactive nucleus which is unstable by emitting radiation?
The answer is no.
That’s what we say when we choose to assert that the dynamic that drives the world is discontinuous.
This does not mean that there would never cases where these discontinuities are sufficiently regular to allow to write a law apparently continues.
This continuity is not apparent then a description of reality, but only an average value of the phenomena that we pretend to add up.
When talking about the fluid dynamics of the assumption of continuity, there is no question of physicists who would assume that the fluids are not comprised of discrete units, the molecules, of course, but only the assumption that a particular phenomenon shows no holes too large to where the phenomenon is observed.
Fluid physicists who talk about "continuo hypothesis" mean that one can assume that "every material point which is infinitely close to another material point will remain so in the future".
However, anyone who has observed the grains in a ray of light knows that this assumption is false continuo although it works well in mathematics.
As for the continuity analysis, a function "jumps", it means that the points very close to the original space, find themselves on very distant points on arrival.
Now, for a continuous, these jumps are not possible, because if one considers a point of departure and arrival image, we know that a whole neighborhood of this starting point must come near the end point!
In this sense, regarding the fundamental meaning of reality, matter as energy, continuity does not exist.
That is what quantum physics says that property, in addition, that any measure is itself flawed by a fundamental discontinuity (problem of measurement)!