| Symbol | Example | Interpretation |
|---|---|---|
| \(\sim\) | \(\tilde{a}\) | Reciprocal of \(a\): \(1/a\) respectively \(a^{-1}\) for \(a \ne 0\) (read as “turn”) |
| \(\acute{}\) | \(\acute{a}\) | Decrement of \(a\): \(a – 1\) (read as “dec”) |
| \(\grave{}\) | \(\grave{a}\) | Increment of \(a\): \(a + 1\) (read as “inc”) |
| \(\hat{}\) | \(\hat{a}\) | Double of \(a\): \(2a\) (read as “hat”) |
| \(\check{}\) | \(\check{a}\) | Half of \(a\): \(a/2\) (read as “half”) |
| \(\text{-}\) | \(a\text{-}\) | \(a\) negated: \(a\text{-}\) (read as “neg”) |
| \(\leftharpoonup\) | \(\overset{\leftharpoonup}{a}\) | Predecessor of \(a\) (read as “pre”) |
| \(\rightharpoonup\) | \(\overset{\rightharpoonup}{a}\) | Successor of \(a\) (read as “post”) |
| \({}_{\times}\) | \(a_{\times n}\) | \(n\)-fold repetition of \(a\) as \((a, \dots, a)^\top\) (read as “rep”) |
| \(\_\) | \(\underline{a}\) | Product of imaginary unit \(\underline{1}\) by \(a \in {\mathbb{R}}^*\) (read as “im”) |
| \(\epsilon\) | \(\epsilon^{\underline{\pi}} = 1\text{-}\) | Euler’s number (read as “eps”) |
| \(\iota\) | \({\mu}_{\iota}\) | Smallest positive real number: \(\iota := \min \mathbb{R}_{>0}\) and standard measure \({\mu}_{\iota}\) |
| \(\nu\) | \({}^{\nu} A\) | Greatest finite number: \(A \in \mathbb{K} \in \{\mathbb{C}, \mathbb{R}\}\) |
| \(\omega\) | \({}^{\omega} A\) | Greatest mid-finite number: \(A \cap {}^{\omega}\mathbb{C} := [-\omega, \omega] + \underline{1}[-\omega, \omega]\) for \(A \in \mathbb{K}\) |
| \(\infty\) | \(\infty \gg \tilde{\iota}^2\) | Replacing \(\pm 0\) by \(\pm\widetilde{\infty}\) as well as \(A_{\infty} := A \cup \{\pm\infty\}\) for the set \(A \subseteq \mathbb{R}\) |
| \(\mathbb{M}\) | \({\mathbb{M}}_{\mathbb{K}}\) | Sets of mid-finite numbers: \({\mathbb{M}}_{\mathbb{R}} := {}^{\omega}{\mathbb{R}}{\setminus}{}^{\nu}{\mathbb{R}}\) and \({\mathbb{M}}_{\mathbb{C}} := {\mathbb{M}}_{\mathbb{R}} + \underline{\mathbb{M}}_{\mathbb{R}}\) |
| \({}^{\dot{}}\) | \(\dot{A}\) | Point-symmetric set of \(A\) (read as “point”) |
| \(\downarrow\) | \({\downarrow}x\) | Differential of \(x\) (read as “down”) |
| \(\uparrow\) | \({\uparrow}f(x){\downarrow}x\) | Integral of \(f(x)\) (read as “up”) |
| \({}^n\) | \({}^n a\) | \(n\)-th derivative \(a^{(n)}\) of \(a\) (read as “n of a”) |
| \({}_b\) | \({}_b a\) | Logarithm \(\log_b a\) to base \(b\) for \(a \in \mathbb{C}{\setminus}\mathbb{R}_{\le 0}\) (read as “b log a”) |
| \({}_1\) | \({}_1 x\) | Unit vector \(x/\lVert x\rVert\) for \(x \ne 0\) (read as “1 vec x”) |
| \(\complement\) | \(\complement_{(m=)1}^n\;a_m\) | Concatenation (read as “con”) of the \(a_m\) to \(a_1, \dots, a_n\) |
| \({\LARGE{\textbf{$\times$}}}\) | \({\LARGE{\textbf{$\times$}}}_{(m=)1}^n{a_m}\) | Product of \(a_1\) up to \(a_n\) |
| \({\LARGE{\textbf{+}}}\) | \({\LARGE{\textbf{+}}}_{(m=)1}^n{a_m}\) | Sum of \(a_1\) up to \(a_n\) |
| \({\LARGE{\textbf{$\pm$}}}\) | \({\LARGE{\textbf{$\pm$}}}_{(m=)1}^n{a_m}\) | Alternating sum of \(a_1\) up to \(a_n\) negating the second summand |
| \({\LARGE{\textbf{$\mp$}}}\) | \({\LARGE{\textbf{$\mp$}}}_{(m=)1}^n{a_m}\) | Alternating sum of \(a_1\) up to \(a_n\) negating the first summand |
| \(\Box\) | ditto | End of proof |
| \(\triangle\) | ditto | End of definition |
© 2024-2026 by Boris Haase