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Results of Research with Music

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# List of Symbols

Symbol Usage Interpretation Note ~LaTeX HTML Unicode
~$$\tilde{a}$$Reciprocal of $$a$$: $$1/a$$ resp. $$a^{-1}$$ for $$a \ne 0$$ (read as “turn”)\widetilde{}U+007E
$$\acute{}$$$$\acute{a}$$Decrement of $$a$$: $$a – 1$$ (read as “dec”)\acute{} U+00B4
$$\grave{}$$$$\grave{a}$$Increment of $$a$$: $$a + 1$$ (read as “inc”)\grave{} U+0060
^$$\hat{a}$$Double of $$a$$: $$2a$$ (read as “hat”)\widehat{}U+0302
$$\check{}$$$$\check{a}$$Half of $$a$$: $$a/2$$ (read as “half”)\widecheck{}U+02C7
$$\text{-}$$$$a\text{-}$$$$a$$ negated: $$a\text{-}$$ (read as “neg”)\text{-}U+002D
_$$z = a + \underline{b}$$Complex part of $$z$$: $$\underline{1}b$$ with imaginary unit $$\underline{1}$$ (read as “comp”)\underline{}U+005F
$$\nu$$$${}^{\nu} A$$greatest         finite number: intersection of the complex or real set $$A$$ for $${}^{\nu}\mathbb{C} := [-\nu, \; \nu] + i[-\nu, \nu]$$\nu&nu;U+03BD
$$\omega$$$${}^{\omega} A$$greatest mid-finite number: intersection of the complex or real set $$A$$ mit $${}^{\omega}\mathbb{C} := [-\omega, \omega] + i[-\omega, \omega]$$\omega&omega;U+03C9
$$\iota$$$$\iota = \min \mathbb{R}_{>0}$$smallest positive real number\iota&iota;U+03B9
$${}_b$$$${}_b a = \log_b a$$Logarithm to base $$b$$ for $$a \in \mathbb{C} \setminus \mathbb{R}_{\le 0}$$ (read as “b log a”){}_b
$${}_1$$$${}_1 x = x/||x||$$Unit vector to $$x \ne 0$${}_1
$$\infty$$$$\infty \gg \tilde{\iota}^2$$Replacing $$\pm0$$ by $$\pm\widetilde{\infty}$$Infinity\infty&infin;U+221E
$$\mathbb M$$$${\mathbb{M}}_{\mathbb{R}} = {}^{\omega}{\mathbb{R}} \setminus {}^{\nu}{\mathbb{R}}$$mid-finite numbers: $${\mathbb{M}}_{\mathbb{C}} := {\mathbb{M}}_{\mathbb{R}} + i{\mathbb{M}}_{\mathbb{R}}$$\mathbb{M}𝕄U+1D544
$${}^{\dot{}}$$$$\dot{A}$$point-symmetric set $$A$$ \dot˙U+02D9
$${}^{\ll}$$$$A^{\ll}$$Set $$A$$ without boundary $$\partial A$$ given by min $$\{d(x, y) : x \in A°, y \in A^{\prime}\} = \tilde{\nu}$$ {}^{\ll}U+226A
$$‘$$$$A’$$Complement of the set $$A$$ComplementU+0027
$$\leftharpoonup$$$$\overset{\leftharpoonup}{a}$$Predecessor of $$a$$ (read as “pre”) \leftharpoonup U+21BC
$$\rightharpoonup$$$$\overset{\rightharpoonup}{a}$$Successor of $$a$$ (read as “post”) \rightharpoonup U+21C0
$$\upharpoonleft$$$$a{\upharpoonleft}_n$$$$n$$-fold repetition of $$a$$ in the form $$(a, … , a)^T$$ (read as “rep”)\upharpoonleftU+21BF
$$\upharpoonright$$$$a{\upharpoonright}_n$$Projection of $$(a_1, … , a_n)^T$$ onto the $$k$$-th entry $$a_k$$ (read as “proj”) \upharpoonright U+21BE
$$\downarrow$$$$\downarrow x$$Differential of $$x$$ (read as “down”)\downarrow&darr;U+8595
$$\uparrow$$$$\uparrow f(x)\downarrow x$$Integral of $$f(x)$$ (read as “up”)\uparrow&uarr;U+8593
$$\Box$$End of proof\BoxU+25A1
$$\triangle$$End of definition\triangle&Delta;U+2206