Beautiful Mathematics of “The King”

Between Zero and One

Lee Gon has been mentioning the phrase, “between zero and one.” But what exactly is the significance of being between zero and one?

A thread
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@ActorLeeMinHo

In episode 3, part 43:16, Lee Gon wrote mathematical formulas on the windows of his hotel suite.
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A viewer seeing this could easily feel intimidated and just dismiss it, but the second line of this mathematical jargon is quite an interesting part.
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It has two major parts (or functions), which can be denoted as the following:
The first function, A, takes the natural logarithm of n, while B is the sum of the series of 1/n. Note that these two functions are different in nature.
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For some analogy, we can think of A as Lee Gon and B as Tae Eul – they come from very different backgrounds, from two different worlds.
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If these two functions are plotted on the same graph, it would look like this:
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The behavior of these two functions is quite interesting. They have different natures, as A is based on the natural logarithm, while B is a sum of a series, but their trajectories are very much similar. With increasing n, they somewhat behave like parallel lines.

We can think of this as an illustration of the lives of Lee Gon and Tae Eul. They have their own lives and worlds. But it seems that through time, they are going in the same direction, like parallel lines. But the sad thing about parallel lines is that they would never meet.

In Mathematics, limits of functions are taken to determine the eventual value such function. For simplicity, it can be thought of as, through time, what value can we expect from such function.
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For functions A and B above, their limit is infinity, that is, they have no limit - they increase indefinitely with increasing n. In other words, the functions diverge.
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As Lee Gon and Tae Eul have their own lives in their own worlds, through time, they diverge.
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The original mathematical statement that Lee Gon wrote actually took the limit of the combined functions. In terms of A and B, it could be simply written as:
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If the combined function, A-B, is plotted, it would look like this:
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What this statement and graph say is that the limit of the combined function, A-B, is between 0 and 1. As the graph illustrates, the function somewhat stabilizes between 0 and 1. In other words, the combined function converges, between 0 and 1.
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Lee Gon and Tae Eul may have different lives, and when left on their own separate worlds, they diverge. But when together, they converge, between 0 and 1.
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Also, in the place between 0 and 1, Tae Eul planted the seeds of imaginary flowers from the Kingdom of Corea. With no wind, rain, nor time, the seeds may never bloom; just as her and Lee Gon coming from different worlds, they may never be together.
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But she had faith enough as she sowed the seeds of their love, and with that love, they would eventually converge between 0 and 1.
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The math statement Lee Gon wrote is rather intimidating, but when analyzed, it gives the story much more depth and meaning. Kim Eun Sook is brilliant in leaving this rather insightful clue in the form of a math statement, which has a solution and answer that are both beautiful

Other threads on "The King"
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