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P10_NUMBERS_23_OCTOBER_2022_COPY.html
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<hr>
<p><strong>NUMBERS_23_OCTOBER_2022_COPY</strong></p>
<hr>
<p>* * *</p>
<p>START OF WEB PAGE COPY</p>
<p>* * *</p>
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<p><strong>NUMBERS</strong></p>
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<figure class="wp-block-image size-full"><img src="https://karlinaobject.files.wordpress.com/2022/07/number_sets_diagram.png?w=1000" alt="" class="wp-image-16828"></figure>
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<p>image_link: <a style="background:#000000;color:#ff9000;" href="https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/number_sets_diagram.png" target="_blank" rel="noopener">https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/number_sets_diagram.png</a></p>
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<p><span style="background:#00ffff;">“Nature is identical to infinity.” – karbytes</span></p>
<hr>
<p><span style="background:#ffff00;">The following terms and their respective definitions (and elaborating paragraphs) attempt to enumerate all possible quantities (i.e. <strong>numbers</strong>). A number is a precisely communicable piece of information which represents exactly one discrete quantity.</span></p>
<p><strong><em>To view hidden text inside of the preformatted text boxes below, scroll horizontally.</em></strong></p>
<hr>
<p><strong>ONE:</strong> (represented by the character <strong>1</strong>) the smallest natural number; the length of the line segment whose endpoints are adjacent integers within a <a style="background:#000000;color:#00ff00;" href="https://karlinaobject.wordpress.com/point_object/" target="_blank" rel="noopener">Cartesian grid</a>.</p>
<hr>
<p><strong>ZERO:</strong> (represented by the character <strong>0</strong>) the absence of quantitative measurement; the integer which represents the halfway point between negative one (-1) and one (1); the point which is the same distance apart from the point labeled -1 as it is apart from the point labeled 1 on the same Cartesian grid axis.</p>
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<p><strong>NUMBER:</strong> a piece of information which represents a finite quantity; a piece of information which can be encoded as a finite sequence of <a style="background:#000000;color:#00ff00;" href="https://karlinaobject.wordpress.com/binary_to_decimal/" target="_blank" rel="noopener">binary digits</a> (i.e. 0 and 1).</p>
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<p><strong>INFINITY:</strong> a direction of perpetual increase; <span style="background:#00ffff;">the instantiation of limitlessly many copies of exactly one <a style="background:#000000;color:#ff9000;" href="https://karlinaobject.wordpress.com/identity/" target="_blank" rel="noopener">pattern</a>; the instantiation of limitlessly many objects such that each one of those objects is <a style="background:#000000;color:#ff9000;" href="https://karlinaobject.wordpress.com/nature/" target="_blank" rel="noopener">phenomenally</a> distinct from every other one of those objects</span>; a “quantity” which is larger than or equal to the sum of all positive numbers (and that “quantity” is not technically a number and there are limitelessly many numbers which would comprise that hypothetical sum (which means that the sum is also technically not a number because that sum cannot be computed by an <a style="background:#000000;color:#ff9000;" href="https://karlinaobject.wordpress.com/agency/" target="_blank" rel="noopener">information processing agent</a> within a finite interval of time if the process of adding each positive number to a running total takes a finite and nonzero amount of <a style="background:#000000;color:#00ff00;" href="https://karlinaobject.wordpress.com/count_down_timer/" target="_blank" rel="noopener">time</a> and a finite and nonzero amount of <a style="background:#ff9000;color:#000000;" href="https://en.wikipedia.org/wiki/Energy" target="_blank" rel="noopener">energy</a> to complete)).</p>
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<p><strong>NATURAL_NUMBER:</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of every unique sum of one or multiple instances of one.</p>
<pre>length("") = 0. // zero (i.e. the quantity which symbolically represents the detection of some noumenon)
length("X") = 1. // smallest natural number (i.e. the quantity which symbolically represents the detection of some phenomenon)
length("XX") = 2 = (1 + 1). // second smallest natural number
length("XXX") = 3 = (2 + 1) = (1 + 2) = ((1 + 1) + 1) = (1 + (1 + 1)). // third smallest natural number
</pre>
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<p><strong>INTEGER:</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of each natural number, each natural number multiplied by negative one, and zero.</p>
<pre>/**
* array represents a finite interval of some
* Cartesian grid axis (i.e. the interval whose
* endpoints are -3 and 3) which is partitioned
* into 6 equally-sized subintervals.
*
* |
* <-- (-3) -- (-2) -- (-1) -- (0) -- (1) -- (2) -- (3) -->
* |
*/
array := [-3, -2, -1, 0, 1, 2, 3]. // absolute_value((-3) - (3)) = absolute_value((3) + (-3)) = absolute_value((-6)) = 6.
subarray_0 := [-3,-2]. // absolute_value((-3) - (-2)) = absolute_value((-3) + (2)) = absolute_value((-1)) = 1.
subarray_1 := [-2, -1]. // absolute_value((-2) - (-1)) = absolute_value((-2) + (1)) = absolute_value((-1)) = 1.
subarray_2 := [-1, 0]. // absolute_value((-1) - (0)) = absolute_value((-1) + (0)) = absolute_value((-1)) = 1.
subarray_3 := [0, 1]. // absolute_value((0) - (1)) = absolute_value((0) + (-1)) = absolute_value((-1)) = 1.
subarray_4 := [1, 2]. // absolute_value((1) - (2)) = absolute_value((1) + (-2)) = absolute_value((-1)) = 1.
subarray_5 := [2, 3]. // absolute_value((2) - (3)) = absolute_value((2) + (-3)) = absolute_value((-1)) = 1.
</pre>
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<p><strong>RATIONAL_NUMBER:</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of each integer and each ratio, (A/B), whose numerator is any integer, A, and whose denominator is any nonzero integer, B.</p>
<pre>Let A be any integer.
Let B be any nonzero integer.
By definition, the ratio (A/B) is a rational number.
</pre>
<pre>is_rational_number(1/3) = true.
is_rational_number(1/1) = true.
is_rational_number(square_root(2)) = false.
is_rational_number(square_root(1)) = true. // square_root(1) = 1.
is_rational_number(square_root(0)) = true. // square_root(0) = 0.
is_rational_number(square_root(-1)) = false. // i := square_root(-1). // i is an imaginary number. Each rational number is a real number.
is_rational_number(0/1) = true. // (0/1) = 0.
is_rational_number(0/0) = false. // Infinity is not a number.
is_rational_number(1/0) = false. // Infinity is not a number.
</pre>
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<p><strong>IRRATIONAL_NUMBER:</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of real numbers which cannot be represented as a fractions whose numerator is an integer and whose denominator is a nonzero integer.</p>
<p>An example of an irrational number is <a style="background:#000000;color:#00ff00;" href="https://karlinaobject.wordpress.com/golden_ratio_approximation/" target="_blank" rel="noopener">the golden ratio</a> (i.e. (1 + square_root(2)) / 5).</p>
<p>Another example of an irrational number is <a style="background:#000000;color:#00ff00;" href="https://karlinaobject.wordpress.com/pi_approximation/" target="_blank" rel="noopener">Pi</a> (i.e. the radius of a circle divided by its diameter).</p>
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<p><strong>REAL_NUMBER</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of numbers which are each not the product of square_root(-1) multiplied by either a rational number or else an irrational number.</p>
<hr>
<p><strong>IMAGINARY_NUMBER</strong> an element of the indefinitely large set (and hypothetically infinitely large set) whose elements consist exclusively of numbers which are each the product of square_root(-1) multiplied by either a rational number or else an irrational number.</p>
<pre>i := square_root(-1). // imaginary number
(i * i) = -1. // real number
((i * i) * i) := ((-1) * i). // imaginary number
</pre>
<hr>
<p><strong>COMPLEX_NUMBER:</strong> the sum of a real number an an imaginary number.</p>
<pre>(2 * i) + 3. // complex number
(2 * i). // imaginary number
(1 * i). // imaginary number
(0 * i) = 0. // real number
</pre>
<hr>
<p>This web page was last updated on 18_OCTOBER_2022. The content displayed on this web page is licensed as <a style="background:#000000;color:#ff9000;" href="https://karlinaobject.wordpress.com/public_domain/" target="_blank" rel="noopener">PUBLIC_DOMAIN</a> intellectual property.</p>
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<p>* * *</p>
<p>END OF WEB PAGE COPY</p>
<p>* * *</p>
<hr>
<p>This web page was last updated on 23_OCTOBER_2022. The content displayed on this web page is licensed as <a style="background:#000000;color:#ff9000;" href="https://karlinaobject.wordpress.com/public_domain/" target="_blank" rel="noopener">PUBLIC_DOMAIN</a> intellectual property.</p>
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