Take for example the example of a 1d line projecting into a 0d point. The line, while infinite, has nowhere to go and in effect must folded in upon itself if it is to exist considering the line can only project if there is somewhere for it project to. In these respects, it must project towards itself, however the problem occurs in the respect the line as an extradimensional entity cannot project back towards its origins. Considering the line alone exists, it acts as its own standard of measurement where any self-relation observes the lines existing through the line. In these respects as it approaches the 0d point the line condenses and expands simultaneously at the same time in different respects. It condenses into a fractal, relative to its original state while expanding through multiplication in a separate respect.

In simpler terms, the continual condensation of the line into a fractal, as a frequency, observes the line continually multiplying in a separate respect as it shrinks. Relative to the original line this contraction, through simultaneous division and multiplication, cause the progress of the line into a continual frequency which in effect condenses into a new line relative to the original as horizontal.

In these respects the continual alternation of the line cause its continual condensation to have an increase in the number of lines, through the frequency, while in the a separate respect each line as a frequency continually shrinks in length relative to the original line. So the frequency of 1/5 inverted to 5 lines is much greater in size than the frequency of 1/100 inverted to 100 lines, where while the number of lines as 5<100 the fraction 1/5>1/100. The frequency of 1/(n→∞) exists as a line infinitely smaller than the original when viewed as a horizontal projection relative to the original.

However this frequency is continually directed towards zero ad-infinitum and hence has an infinite progression. This infinite progression observes the line as continually projecting towards point 0 with the increase in the number of lines as (n→∞)→0.

## (n→∞) → 0

### Re: (n→∞) → 0

I don't follow your mysticism. Consider the function f(x) = 0 defined for all real numbers x. This function maps the entire real line to the point zero. If you like we can visualize it geometrically as squeezing the real line down to a point.

Now what of it? This isn't that big a deal. I don't follow the rest of it.

ps -- Same thing for f(x) = c for any real number constant c. All you're doing is getting yourself all worked up about the constant functions.

### Re: (n→∞) → 0

All numbers approaching infinity simultaneously approach 0, it means all whole numbers directed away from zero in effect return back to it.wtf wrote: ↑Fri Jul 13, 2018 5:54 amI don't follow your mysticism. Consider the function f(x) = 0 defined for all real numbers x. This function maps the entire real line to the point zero. If you like we can visualize it geometrically as squeezing the real line down to a point.

Now what of it? This isn't that big a deal. I don't follow the rest of it.

ps -- Same thing for f(x) = c for any real number constant c. All you're doing is getting yourself all worked up about the constant functions.

Actually it is not mysticism if looking at the nature of number:

All numbers, as the quantification of empirical realities are premised at minimum in a Euclidian 1 dimensional line as the act of quantification is the act of observing direction. If I observe an orange and I quantify it as one, what I am doing is observing it project in one direction through time. 1 is inescapable in these respects from the line considering quantity is in effect premised in empirical observation.

1 as directional in effect gives us a different understanding of number if we observe the folding of the line through frequencies. Frequencies in effect act as whole numbers and fractals simultaneously under this understanding of 1 as directional....or numbers exist through frequencies. This alternation inherent within the number is inevitable.

So lets say we observe a line folding in half to form an angle. This 1 line folds in half to form 2 lines as 1/2 through an angle. This line in turn folds to 1/3 of itself as 3 lines resulting in two alternating angles as a frequency. This progress continues ad-infinitum until you have a frequency observing both a whole number approaching infinity and a fraction of 1 divided by a number approaching infinity.

This frequency in effect becomes denser and denser where relative to the other frequencies it in effect becomes a line again. In a seperate respect this continual folding of the line, resulting in both whole numbers and fractals, causes the frequency to take on a directional role where it continually projects in effect to point zero.

In effect is observes that while a number line may observe all whole numbers approaching infinity, this infinity in effect is projecting back to point zero. The number line extends from point zero and ineffect returns to point zero so the whole "linear" approach to the number line, and numbers in general leads it back to a cycle.

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