Mineral Set
Can mineral hardness be expressed as a theory of sets in analysis?
Yo. I'm not sure of the likelihood of getting an answer, but I'll stab nonetheless...
I'm a student in geology with a reasonable background in physics and math and I'm interested in pursuing study in Mohs hardness scale. The problem with the scale is that it is relative - a diamond is a 10 on the scale, for example, only because of a "scratch test"; it scratches quarzt, which scratches somethinbg else, etc...
Basically, what I want to do is express hardness in an absolute sense as a differrential function of set theory, in which the mineral's the subset, it's forces are it's elements, all forces are the set, and the breaking point of the mineral is the upper-bound element in the set.
What I want to kow is: a). Does this sound plausible? b). Aside from stress physics and continuity functions, what else would I need to know? I'm kind of going out on the limb outside of the department to present this here. Thanks for the time.
Peace.
No, you can't express the Moh hardness scale as anything but what it already is. Ten minerals were chosen with respect to their relative hardness but no thought was given to possibly giving a log scale or any linear increase in hardness. In addition to that, composition can't be used as a basis for expressing the scale because pure carbon is present in graphite form and diamond form and they're complete opposites in the hardness scale. There are many other problems with your attempt. Sorry.
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