τ also represents the topology on a set; the set that defines the structure of the original set (Example usage: (𝑋, τ) wherein 𝑋 is a set, and τ is the set of some of the subsets from 𝑋) The symbol alongside π and φ is also usually used to denote a mapping between sets in modern algebra and topology (Example usage: π: A→B or τ: A→B wherein A and B are sets, and if a is an element from A, then π(a) or τ(a) is an element from B) Speaking of φ, it's also used to denote the azimuthal angle in spherical coordinates, which is made up with ρ and θ (Example usage: ρcos(θ)sin(φ)î + ρsin(θ)sin(φ)ĵ + ρcos(φ)k̂ in 3D-space is the sphere of radius ρ from the origin) ζ and ω are also used to denote nth roots of unity, which are equations of the form ζⁿ = 1 or ωⁿ = 1, wherein ζ or ω is some complex number, and n is an integer. (Example usage: ω³ = 1 means ω = -1/2 + i√3/2) λ is less commonly but in a more general case from the eigenvalue usage, is also used in linear algebra to denote a scalar value from the ground field (This is usually the reals) of a vector space (Usually the set of all n-tuples of real numbers) (Example usage: λ₁e₁ + λ₂e₂ + λ₃e₃ + λ₄e₄ denotes a linear combination of the vectors e₁ through e₄, and λ₁ through λ₄ are real numbers)
Bonus: sigma = axial stress (force/area in an element under tensile or compressive load) epsilon = axial strain (current length/original length of element) tau = shear stress (like axial stress but the load acts parallel to the stress plane) gamma = shear strain (change in angle of a line originally perpendicular to shear plane) phi = angle when theta is already used psi = angle when both theta and phi are used rho = density omega = angular velocity zeta (or "snake," according to my professor who can't draw it properly) = damping ratio of mass-spring-damper system
now i can speak fluent greek
Οφςομρσε, μι φριεηδ
τ also represents the topology on a set; the set that defines the structure of the original set (Example usage: (𝑋, τ) wherein 𝑋 is a set, and τ is the set of some of the subsets from 𝑋)
The symbol alongside π and φ is also usually used to denote a mapping between sets in modern algebra and topology (Example usage: π: A→B or τ: A→B wherein A and B are sets, and if a is an element from A, then π(a) or τ(a) is an element from B)
Speaking of φ, it's also used to denote the azimuthal angle in spherical coordinates, which is made up with ρ and θ (Example usage: ρcos(θ)sin(φ)î + ρsin(θ)sin(φ)ĵ + ρcos(φ)k̂ in 3D-space is the sphere of radius ρ from the origin)
ζ and ω are also used to denote nth roots of unity, which are equations of the form ζⁿ = 1 or ωⁿ = 1, wherein ζ or ω is some complex number, and n is an integer.
(Example usage: ω³ = 1 means ω = -1/2 + i√3/2)
λ is less commonly but in a more general case from the eigenvalue usage, is also used in linear algebra to denote a scalar value from the ground field (This is usually the reals) of a vector space (Usually the set of all n-tuples of real numbers) (Example usage: λ₁e₁ + λ₂e₂ + λ₃e₃ + λ₄e₄ denotes a linear combination of the vectors e₁ through e₄, and λ₁ through λ₄ are real numbers)
Bonus:
sigma = axial stress (force/area in an element under tensile or compressive load)
epsilon = axial strain (current length/original length of element)
tau = shear stress (like axial stress but the load acts parallel to the stress plane)
gamma = shear strain (change in angle of a line originally perpendicular to shear plane)
phi = angle when theta is already used
psi = angle when both theta and phi are used
rho = density
omega = angular velocity
zeta (or "snake," according to my professor who can't draw it properly) = damping ratio of mass-spring-damper system
Also Epsilon Denotes A Universal Set
In set theory
some of them are more physics than math
That thumbnail hurt my soul in all the ways
Why?
Lower Sigma can also represent permutations of finite sets {1,2,3, ... n}.
Ah yes, my favorite ordinal “1th”
0:33
Are you using some kind of AI for the voice? Aside from the butchered pronunciations of names, you pronounced a+bi like “a plus bye”. Wtf.
8 was thinking the same thing.
O is also used to denote the origin
I remember learning Greek alphabet for maths few years ago which kind of helped me remembering formula in maths and physics lol
0:34 literally man
Almost all the Greek letters were mispronounced.
rho, rho, rho your boat
gently down the ρεύμα
I love the Sibelius
wheres my lowercase sigma function
or my prime counting function
or somos' quadratic recurrence constant
a plus bye 😂
π can also represent an arbitrary permutation m, for example, in linear algebra when talking about the determinant.
capital omega is used for absolute infinity but I guess this isn't used in math
bro fell off
NO EULER PHI FUNCTION???
Ω
Badenerie in the background 😭
My prof uses xi or small epsillon for an and symbol lol.
Sigma rizzler
Ψ
"Firth" 🎉
δ ε
Ψω
8:44 “poler “ LOL really???? You speak English right? Try Polar!
1st
Oneth
1th