Proportionality and Countability
There is proportionality in discrete countability -
What is 5x? x+x+x+x....5 times. This is equivalent to multiplying the number 5 with x.
Now, what is 2.2x? You can't directly say that it is x + x + .. 2.2 times because - how can the number of times be 2.2? But you can indeed say it actually. Its x + x + 0.2x i.e. one whole x plus one whole x plus 0.2th of x. So, in the third term, instead of a whole ONE x, you have taken a PROPORTIONAL quantity of x which is 0.2th of an x or (x/5) and this works well in the counting scheme above of 2.2x being x + x +..."2.2 TIMES" or the third term being "0.2 TIMES" even if it (0.2) is not a discrete unity integer.
So countability (which is additive) is consistent with proportionality (which is multiplicative).
Labels: General / Philosophy
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