- #26

collinsmark

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Why do I believe this? Because 1 divided 3 is an human created impossible description of a possible reality. Here is an example. If you take three lines, each measuring 2 feet exactly and combine them into one line, you get a single line measuring 6 feet.

If 6 feet equals 1 Unit, then the result of 1 Unit divided by 3 is an impossible mathmatical description of the actual length because we know for a fact that that single line divided by 3 WILL equal three lines of exact measure.

In one context, the lines are equal and in another they are not. This is a mathmatical paradox and proves that math is actually relative to human perception and perspective.

I don't see any paradox at all. And this is even without having to express an infinite number of numerals in the decimal precision (i.e., 0.333...) or expressing values as fractions (i.e., 1/3).

1

_{(base 10)}is 1

_{(base 3)}.

2

_{(base 10)}is 2

_{(base 3)}.

3

_{(base 10)}is 10

_{(base 3)}.

6

_{(base 10)}is 20

_{(base 3)}.

So we have three lines, each 2

_{(base 3)}feet long.

We add three of them together:

2

_{(base 3)}+ 2

_{(base 3)}+ 2

_{(base 3)}[feet] = (2

_{(base 3)}[feet])(10

_{(base 3)}) = 20

_{(base 3)}[feet].

Let's call that one Unit.

1 Unit = 20

_{(base 3)}feet.

Now let's divide that by three (decimal), [recalling 3

_{(base 10)}is 10

_{(base 3)}].

1

_{(base 3)}Unit / 10

_{(base 3)}= 0.1

_{(base 3)}Units each.

(And by the way, 0.1

_{(base 3)}= (1/3)

_{(base 10)}.)

Converting to feet, each of the three lines has length

(0.1

_{(base 3)}Unit)(20

_{(base 3)}feet/Unit) = 2

_{(base 3)}feet

No paradox there.

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