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Replies: 23   Last Post: Jul 10, 2014 10:00 PM

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 Brian Q. Hutchings Posts: 6,427 Registered: 12/6/04
Posted: Jul 6, 2014 2:15 PM

that is kind of cute, but I don't see that it
is not strictly isomorphic with a)
Euclid's usage, and b)
the standard, modern usage

> A unit is the result of a ratio where the magnitudes are equal, that is, x:x, y:y, u:u, etc.
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> This was a quantum leap in the development of number. From the abstraction of the unit, one now has a standard of measurement. Having established the unit, quantitative trichotomy is now possible. For example, if any two magnitudes are composed of units (or multiples of units), then it is possible to tell the difference in terms of units. Think of this with relation to the ratio of magnitudes where it is only possible to tell if equal, greater or smaller, BUT NOT by how much greater or smaller.
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> The stage was now set for the final step. What to do if a magnitude is a measurable part of a unit?
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> This led to the establishment of the fraction - a ratio of natural numbers where natural numbers are composed of units.
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> The anti-climax became manifest when ancient mathematicians discovered that certain magnitudes refused to be measured in units or parts of a unit. These were called the incommensurable magnitudes.
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> If you were able to comprehend this comment in its entirety, then you already know more than all the mathematics professors combined with regards to number. In fact, you will have understood and learned more than you did in all your school years.
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> To learn more and increase your knowledge of mathematics, I recommend you study my New Calculus - the first and only rigorous formulation of calculus in human history. http://thenewcalculus.weebly.com
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> Comments are NOT welcome. This comment is produced in the interests of public education; and to eradicate ignorance and stupidity from mainstream mathematics.