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I learned a little about these concepts in a pure mathematical book.

I was thinking about their utility in physics.. I know they probably do.. What physical areas could these concepts be used in?

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In summary, the conversation discusses the concepts of continuous groups and their utility in physics. The speaker mentions learning about these concepts in a mathematical book and being unsure of their application in physics. Examples and calculations are requested to clarify the discussion.

- #1

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I learned a little about these concepts in a pure mathematical book.

I was thinking about their utility in physics.. I know they probably do.. What physical areas could these concepts be used in?

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- #2

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Your are very vague. Don't be lazy, give some more information and/or examples.

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but I really don't know of any examples, that's why I'm asking for them.martinbn said:Your are very vague. Don't be lazy, give some more information and/or examples.

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Ok, but it is not clear what you are talking about. Can you at least tell us which book?

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An example of a group you've been given, and an invariant measure, and what a "sum over the group elements" entails, would be useful. Surely some example was given in your textbook. Surely they actually did a calculation when they introduced these things. So show us that calculation.

The density function in physics is a mathematical tool used to describe the distribution of matter within a given volume. It is often denoted as ρ (rho) and is defined as the mass of a substance per unit volume.

The density function is used in various areas of physics, such as fluid mechanics, electromagnetism, and thermodynamics. It allows us to calculate important properties such as mass, volume, and pressure of a substance, which are crucial in understanding the behavior of physical systems.

The equation for density function is ρ = m/V, where ρ is density, m is mass, and V is volume. This equation shows that density is directly proportional to mass and inversely proportional to volume.

The density function and specific gravity are related through the equation ρ = ρ_{0} x SG, where ρ_{0} is the density of a reference substance and SG is the specific gravity. This equation allows us to compare the density of a substance to the density of a reference substance, typically water.

The density function has many practical applications, such as determining the buoyancy of objects in water, calculating the mass and volume of a substance for manufacturing purposes, and understanding the behavior of fluids in pipelines and pumps. It is also crucial in fields like geology and oceanography for studying the composition of different materials.

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