Equave limit: Difference between revisions

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==Definition==

The '''q-equave-n-limit''' is defined as the set of all positive rationals ~~<big><big>~~<math>\displaystyle

The '''q-equave-n-limit''' is defined as the set of all positive rationals <math>\displaystyle

{q^z}\cdot\frac{u}{v}

</math~~></big></big~~>, where:

</math>, where:

* <math>~~q∈Q~~+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',

* <math>q \in \mathbb{Q}^{+}</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',

* <math>~~z∈Z~~</math> (i.e., <math>z</math> is an integer, positive or negative),

* <math>z \in \mathbb{Z}</math> (i.e., <math>z</math> is an integer, positive or negative),

* <math>u,~~v∈Z~~+</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>~~u≤n~~</math> and <math>~~v≤n~~</math>,

* <math>u,v \in \mathbb{Z}^{+}</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>u \leqslant n</math> and <math>v \leqslant n</math>,

* <math>~~n∈Z~~+</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.

* <math>n \in \mathbb{Z}^{+}</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.

The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the '''q-equave-n-limit''' consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle

@@ Line 2: / Line 2: @@
 ==Definition==
-The '''q-equave-n-limit''' is defined as the set of all positive rationals <big><big><math>\displaystyle
+The '''q-equave-n-limit''' is defined as the set of all positive rationals <math>\displaystyle
 {q^z}\cdot\frac{u}{v}
-</math></big></big>, where:
+</math>, where:
-* <math>q∈Q+</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',
+* <math>q \in \mathbb{Q}^{+}</math> (i.e., <math>q</math> is a positive rational number), called the '''equave''',
-* <math>z∈Z</math> (i.e., <math>z</math> is an integer, positive or negative),
+* <math>z \in \mathbb{Z}</math> (i.e., <math>z</math> is an integer, positive or negative),
-* <math>u,v∈Z+</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>u≤n</math> and <math>v≤n</math>,
+* <math>u,v \in \mathbb{Z}^{+}</math> (i.e., <math>u</math> and <math>v</math> are positive integers) such that <math>u \leqslant n</math> and <math>v \leqslant n</math>,
-* <math>n∈Z+</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.
+* <math>n \in \mathbb{Z}^{+}</math> (i.e., <math>n</math> is a positive integer), called the '''limit'''.
 The parameter <math>n</math> places an upper bound on the values of the integers <math>u</math> and <math>v</math>, meaning that both <math>u</math> and <math>v</math> are less than or equal to <math>n</math>. Thus, the '''q-equave-n-limit''' consists of ratios generated by multiplying a power of <math>q</math> by ratios <math>\displaystyle