The Azimuth Project
Continuum hypothesis (Rev #4, changes)

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Contents

Idea

The continuum hypothesis in continuum mechanics, and especially hydrodynamics, is the assumption that fluids can be approximately modelled with functions of real numbers. Therefore, (There physical is properties also of a fluids statement are in described set by theory time called dependent the scalar ‘continuum or hypothesis’, vector but fields this on is completely unrelated.)\mathbb{R}.

This The assumption continuum can hypothesis only justifies be our approximately true, of course, since the most accurate description of matter fluids known by today time uses dependent the scalar concept or of vector elementary fields particles on and atoms of particles.\mathbb{R}. This can only be approximately true, of course, since the most accurate description of matter known today uses the concept of elementary particles and atoms of particles.

For liquids, the continuum hypothesis is a good approximation for most practical situations, for gases, the Knudsen number K should be much smaller than one, K1K \ll 1, where K is defined to be K:=λLK:= \frac{\lambda}{L}. λ\lambda is the mean free path of a particle, and LL is the length scale of phenomena that one wishes to describe.

References

There is also a statement in set theory called the ‘continuum hypothesis’, but this is completely unrelated.