Compare the table below to Joe Java’s MathML tests:
| $$∀A∃P∀B\,[B∈P ⇔ ∀C\,(C∈B⇒C∈A)]$$ |
| $$\text"Logic: "¬(p∧q) ⇔ (¬p)∨(¬q)$$ $$\text"Boolean algebra: "{⋃↙{i=1}↖n A_i}↖{\_} = ⋂↙{i=1}↖n {A_i}↖{\_}$$ |
| $$x = {-b±√{b^2-4ac}}/{2a}$$ |
| $$\bo C(n,k) = \bo C_k^n = {_n\bo C_k^} = \binom n k = n!/{k!\,(n-k)!}$$ |
| $$∫_0^1 x^x\,\d x = ∑↙{n=1}↖∞ ({-1})^{n+1}\,n^{-n}$$ |
| $$∇·v↖{→} = ∂v_x/∂x + ∂v_y/∂y + ∂v_z/∂z$$ |
| $$c = { {\sp 1.2em a\sp 1.2em}↙{⏟}↙\text"real" + {\sp 1em b\i\sp 1em}↙{⏟}↙\text"imaginary" } ↖{⏞}↖\text"complex number"$$ |
| $$M = [\table α_1, α_1^q, …, α_1^{q^{n-1}}; α_2, α_2^q, …, α_2^{q^{n-1}}; ⋮, ⋮, ⋱, ⋮; α_m, α_m^q, …, α_m^{q^{n-1}}]$$ |
| Spherical coordinates derivation of the volume of a sphere $(4/3πR^3)$, for a sphere $S$ of radius $R$: $$S = \{ 0≤ϕ≤2π, 0≤θ≤π, 0≤ρ≤R \}$$ $$\cl"ma-join-align"{\table \text"Volume", {= ∭↙S ρ^2 \sin θ\,\d ρ\,\d θ\,\d ϕ}; , {= ∫_0^{2π} \d ϕ\,\,∫_0^π \sin θ\,\d θ\,\,∫_0^R ρ^2\,\d ρ}; , {= {ϕ\sp .11em \minsize 2.5 |_{\sp .11em 0}^{\sp .11em 2π}} \,\,{(-\cos θ)\sp .11em \minsize 2.5 |_{\sp .11em 0}^{\sp .11em π}} \,\,{1/3 ρ^3\sp .11em \minsize 2.5 |_{\sp .11em 0}^{\sp .11em R}}}; , {= 2π × 2 × 1/3 R^3}; , {= 4/3 πR^3}}$$ |
| $$⟨ψ|\sc T\{δ/{δϕ} F[ϕ]\}|ψ⟩ = -\i⟨ψ|\sc T\{F[ϕ] δ/{δϕ} S[ϕ]\}|ψ⟩$$ |
| $$γ_1≡γ_2 ⇔ \{\,\cl"ma-join1-align"{\table γ_1(0) = γ_2(0) = p\text", and"; {\d /{\d t} ϕ \,◦\, γ_1(t)\sp .11em |_{\sp .11em t=0}} = {\d /{\d t} ϕ \,◦\, γ_2(t)\sp .11em |_{\sp .11em t=0}}}$$ |
| $$\cl"thin-column-padding"{\table , , \cov(ℒ), →, \non(\sc K), →, \cof(\sc K), →, \cof(ℒ), →, 2^{ℵ_0}; , , \rowspan 3 \minsize 3 ↑, , ↑, , ↑, , \rowspan 3 \minsize 3 ↑, , ; , , , \fr b, →, \fr d, , , ; , , , ↑, , ↑, , , ; ℵ_1, →, \add(ℒ), →, \add(\sc K), →, \cov(\sc K), →, \non(ℒ), , }$$ |
| $$ {↖ _{_α^β\fr A_δ^γ} ^{_ε^ζ\fr B_θ^η} ∏ _{_ρ^σ\fr E_υ^τ} ^{_ν^ξ\fr D_π^ο} } ↙{_ϕ^χ\fr F_ω^ψ} ↖{_ι^κℭ_μ^λ}$$ |
| $$√{1+√^3{2+√^5{3+√^7{4+√^11{5+√^13{6+√^17{7+√^19A}}}}}}} / \e^\π = x'''$$ |
| $$(\table \rowspan 2 \minsize 2.5{(}, a_1, a_2, , a_3, a_4, \rowspan 2 \minsize 2.5{)}, \rowspan 4 \minsize 5.5{(}, b_1, \rowspan 4 \minsize 5.5{)}; a_5, a_6, , a_7, a_8, b_2; , \cl"matrix-block"{\rowspan 2 \colspan 2 0}, \rowspan 2 \minsize 2.5{(}, c_1, c_2, \rowspan 2 \minsize 2.5{)}, b_3; , c_3, c_4, b_4)$$ |
| 2.8em, 2em, 1.4em, 1em, 0.7em |