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Welcome to the general discussion page of $\mathsf{Pr} \infty \mathsf{fWiki}$.
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Main Talk Page Archives

Archive 1: $-\infty$ to Sept 24/08
Archive 2: Sept 25/08 to Dec 20/08
Archive 3: Dec 21/08 to Feb 21/09
Archive 4: Feb 22/09 to Jun 14/09
Archive 5: Jun 15/09 to Feb 21/10
Archive 6: Feb 22/10 to May 10/11
Archive 7: May 11/11 to Mar 28/12
Archive 8: Mar 29/12 to Oct 10/12
Archive 9: Oct 11/12 to May 18/13
Archive 10: May 27/13 to Oct 18/14
Archive 11: Oct 27/14 to Dec 21/15
Archive 12: Dec 22/15 to Aug 1/17
Archive 13: Aug 2/17 to May 8/18
Archive 14: May 26/18 to Apr 9/20
Archive 15: May 9/20 to Dec 31/21



New $\LaTeX$ macros for your convenience and our internal consistency

There are a number of new $\LaTeX$ macros which have been developed recently as a result of a lot of discussion some time back which never ended up happening at the time.

They can be found on the page Symbols:LaTeX Commands/ProofWiki Specific, transcluded here:


\(\AA\) $\quad:\quad$\AA $\qquad$that is: \mathcal A
\(\Add\) $\quad:\quad$\Add $\qquad$Addition as a Primitive Recursive Function‎
\(\adj {\mathbf A}\) $\quad:\quad$\adj {\mathbf A} $\qquad$Adjugate Matrix
\(\arccot\) $\quad:\quad$\arccot $\qquad$Arccotangent
\(\arccsc\) $\quad:\quad$\arccsc $\qquad$Arccosecant
\(\arcosh\) $\quad:\quad$\arcosh $\qquad$Area Hyperbolic Cosine
\(\Arcosh\) $\quad:\quad$\Arcosh $\qquad$Complex Area Hyperbolic Cosine
\(\arcoth\) $\quad:\quad$\arcoth $\qquad$Area Hyperbolic Cotangent
\(\Arcoth\) $\quad:\quad$\Arcoth $\qquad$Complex Area Hyperbolic Cotangent
\(\arcsch\) $\quad:\quad$\arcsch $\qquad$Area Hyperbolic Cosecant
\(\Arcsch\) $\quad:\quad$\Arcsch $\qquad$Complex Area Hyperbolic Cosecant
\(\arcsec\) $\quad:\quad$\arcsec $\qquad$Arcsecant
\(\arsech\) $\quad:\quad$\arsech $\qquad$Area Hyperbolic Secant
\(\Arsech\) $\quad:\quad$\Arsech $\qquad$Complex Area Hyperbolic Secant
\(\arsinh\) $\quad:\quad$\arsinh $\qquad$Area Hyperbolic Sine
\(\Arsinh\) $\quad:\quad$\Arsinh $\qquad$Complex Area Hyperbolic Sine
\(\artanh\) $\quad:\quad$\artanh $\qquad$Area Hyperbolic Tangent
\(\Artanh\) $\quad:\quad$\Artanh $\qquad$Complex Area Hyperbolic Tangent
\(\Area\) $\quad:\quad$\Area $\qquad$Area of Plane Figure
\(\Arg z\) $\quad:\quad$\Arg z $\qquad$Principal Argument of Complex Number
\(\Aut {S}\) $\quad:\quad$\Aut {S} $\qquad$Automorphism Group
\(\BB\) $\quad:\quad$\BB $\qquad$that is: \mathcal B
\(\Bei\) $\quad:\quad$\Bei
\(\Ber\) $\quad:\quad$\Ber
\(\Bernoulli {p}\) $\quad:\quad$\Bernoulli {p} $\qquad$Bernoulli Distribution
\(\BetaDist {\alpha} {\beta}\) $\quad:\quad$\BetaDist {\alpha} {\beta} $\qquad$Beta Distribution
\(\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a}\) $\quad:\quad$\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a} $\qquad$Limits of Integration
\(\bigvalueat {\delta x} {x \mathop = x_j} \) $\quad:\quad$\bigvalueat {\delta x} {x \mathop = x_j}
\(\Binomial {n} {p}\) $\quad:\quad$\Binomial {n} {p} $\qquad$Binomial Distribution
\(\braket {a} {b}\) $\quad:\quad$\braket {a} {b} $\qquad$Dirac Notation
\(\bsalpha\) $\quad:\quad$\bsalpha
\(\bsbeta\) $\quad:\quad$\bsbeta
\(\bschi\) $\quad:\quad$\bschi
\(\bsDelta\) $\quad:\quad$\bsDelta $\qquad$a vector '$\Delta$'
\(\bsdelta\) $\quad:\quad$\bsdelta
\(\bsepsilon\) $\quad:\quad$\bsepsilon
\(\bseta\) $\quad:\quad$\bseta
\(\bsgamma\) $\quad:\quad$\bsgamma
\(\bsiota\) $\quad:\quad$\bsiota
\(\bskappa\) $\quad:\quad$\bskappa
\(\bslambda\) $\quad:\quad$\bslambda
\(\bsmu\) $\quad:\quad$\bsmu
\(\bsnu\) $\quad:\quad$\bsnu
\(\bsomega\) $\quad:\quad$\bsomega
\(\bsomicron\) $\quad:\quad$\bsomicron
\(\bsone\) $\quad:\quad$\bsone $\qquad$vector of ones
\(\bsphi\) $\quad:\quad$\bsphi
\(\bspi\) $\quad:\quad$\bspi
\(\bspsi\) $\quad:\quad$\bspsi
\(\bsrho\) $\quad:\quad$\bsrho
\(\bssigma\) $\quad:\quad$\bssigma
\(\bst\) $\quad:\quad$\bst $\qquad$a vector 't'
\(\bstau\) $\quad:\quad$\bstau
\(\bstheta\) $\quad:\quad$\bstheta
\(\bsupsilon\) $\quad:\quad$\bsupsilon
\(\bsv\) $\quad:\quad$\bsv $\qquad$a vector 'v'
\(\bsw\) $\quad:\quad$\bsw $\qquad$a vector 'w'
\(\bsx\) $\quad:\quad$\bsx $\qquad$a vector 'x'
\(\bsxi\) $\quad:\quad$\bsxi
\(\bsy\) $\quad:\quad$\bsy $\qquad$a vector 'y'
\(\bsz\) $\quad:\quad$\bsz $\qquad$a vector 'z'
\(\bszero\) $\quad:\quad$\bszero $\qquad$vector of zeros
\(\bszeta\) $\quad:\quad$\bszeta
\(\map \Card {S}\) $\quad:\quad$\map \Card {S} $\qquad$Cardinality
\(\card {S}\) $\quad:\quad$\card {S} $\qquad$Cardinality
\(\Cauchy {x_0} {\gamma}\) $\quad:\quad$\Cauchy {x_0} {\gamma} $\qquad$Cauchy Distribution
\(\CC\) $\quad:\quad$\CC $\qquad$that is: \mathcal C
\(\Cdm {f}\) $\quad:\quad$\Cdm {f} $\qquad$Codomain of Mapping
\(\ceiling {11.98}\) $\quad:\quad$\ceiling {11.98} $\qquad$Ceiling Function
\(30 \cels\) $\quad:\quad$30 \cels $\qquad$Degrees Celsius
\(\Char {R}\) $\quad:\quad$\Char {R} $\qquad$Characteristic of Ring, etc.
\(\Ci\) $\quad:\quad$\Ci $\qquad$Cosine Integral Function
\(\cis \theta\) $\quad:\quad$\cis \theta $\qquad$$\cos \theta + i \sin \theta$
\(\cl {S}\) $\quad:\quad$\cl {S} $\qquad$Closure (Topology)
\(\closedint {a} {b}\) $\quad:\quad$\closedint {a} {b} $\qquad$Closed Interval
\(\cmod {z^2}\) $\quad:\quad$\cmod {z^2} $\qquad$Complex Modulus
\(\condprob {A} {B}\) $\quad:\quad$\condprob {A} {B} $\qquad$Conditional Probability
\(\conjclass {x}\) $\quad:\quad$\conjclass {x} $\qquad$Conjugacy Class
\(\cont {f}\) $\quad:\quad$\cont {f} $\qquad$Content of Polynomial
\(\ContinuousUniform {a} {b}\) $\quad:\quad$\ContinuousUniform {a} {b} $\qquad$Continuous Uniform Distribution
\(\cosec\) $\quad:\quad$\cosec $\qquad$Cosecant (alternative form)
\(\Cosh\) $\quad:\quad$\Cosh $\qquad$Hyperbolic Cosine
\(\Coth\) $\quad:\quad$\Coth $\qquad$Hyperbolic Cotangent
\(\cov {X, Y}\) $\quad:\quad$\cov {X, Y} $\qquad$Covariance
\(\csch\) $\quad:\quad$\csch $\qquad$Hyperbolic Cosecant
\(\Csch\) $\quad:\quad$\Csch $\qquad$Hyperbolic Cosecant
\(\curl\) $\quad:\quad$\curl $\qquad$Curl Operator
\(\DD\) $\quad:\quad$\DD $\qquad$that is: \mathcal D
\(\dfrac {\d x} {\d y}\) $\quad:\quad$\dfrac {\d x} {\d y} $\qquad$Roman $\d$ for Derivatives
\(30 \degrees\) $\quad:\quad$30 \degrees $\qquad$Degrees of Arc
\(\diam\) $\quad:\quad$\diam $\qquad$Diameter
\(\Dic n\) $\quad:\quad$\Dic n $\qquad$Dicyclic Group
\(\DiscreteUniform {n}\) $\quad:\quad$\DiscreteUniform {n} $\qquad$Discrete Uniform Distribution
\(a \divides b\) $\quad:\quad$a \divides b $\qquad$Divisibility
\(\Dom {f}\) $\quad:\quad$\Dom {f} $\qquad$Domain of Mapping
\(\dr {a}\) $\quad:\quad$\dr {a} $\qquad$Digital Root
\(\E\) $\quad:\quad$\E $\qquad$Elementary Charge
\(\EE\) $\quad:\quad$\EE $\qquad$that is: \mathcal E
\(\Ei\) $\quad:\quad$\Ei $\qquad$Exponential Integral Function
\(\empty\) $\quad:\quad$\empty $\qquad$Empty Set
\(\eqclass {x} {\RR}\) $\quad:\quad$\eqclass {x} {\RR} $\qquad$Equivalence Class
\(\erf\) $\quad:\quad$\erf $\qquad$Error Function
\(\erfc\) $\quad:\quad$\erfc $\qquad$Complementary Error Function
\(\expect {X}\) $\quad:\quad$\expect {X} $\qquad$Expectation
\(\Exponential {\beta}\) $\quad:\quad$\Exponential {\beta} $\qquad$Exponential Distribution
\(\Ext {\gamma}\) $\quad:\quad$\Ext {\gamma} $\qquad$Exterior
\(\F\) $\quad:\quad$\F $\qquad$False
\(30 \fahr\) $\quad:\quad$30 \fahr $\qquad$Degrees Fahrenheit
\(\family {S_i}\) $\quad:\quad$\family {S_i} $\qquad$Indexed Family
\(\FF\) $\quad:\quad$\FF $\qquad$that is: \mathcal F
\(\Fix {\pi}\) $\quad:\quad$\Fix {\pi} $\qquad$Set of Fixed Elements
\(\floor {11.98}\) $\quad:\quad$\floor {11.98} $\qquad$Floor Function
\(\fractpart {x}\) $\quad:\quad$\fractpart {x} $\qquad$Fractional Part
\(\Frob {R}\) $\quad:\quad$\Frob {R} $\qquad$Frobenius Endomorphism
\(\Gal {S}\) $\quad:\quad$\Gal {S} $\qquad$Galois Group
\(\Gaussian {\mu} {\sigma^2}\) $\quad:\quad$\Gaussian {\mu} {\sigma^2} $\qquad$Gaussian Distribution
\(\gen {S}\) $\quad:\quad$\gen {S} $\qquad$Generator
\(\Geometric {p}\) $\quad:\quad$\Geometric {p} $\qquad$Geometric Distribution
\(\GF\) $\quad:\quad$\GF $\qquad$Galois Field
\(\GG\) $\quad:\quad$\GG $\qquad$that is: \mathcal G
\(\GL {n, \R}\) $\quad:\quad$\GL {n, \R} $\qquad$General Linear Group
\(\grad {p}\) $\quad:\quad$\grad {p} $\qquad$Gradient
\(\hav \theta\) $\quad:\quad$\hav \theta $\qquad$Haversine
\(\hcf\) $\quad:\quad$\hcf $\qquad$Highest Common Factor
\(\H\) $\quad:\quad$\H $\qquad$Set of Quaternions
\(\HH\) $\quad:\quad$\HH $\qquad$Hilbert Space
\(\hointl {a} {b}\) $\quad:\quad$\hointl {a} {b} $\qquad$Left Half-Open Interval
\(\hointr {a} {b}\) $\quad:\quad$\hointr {a} {b} $\qquad$Right Half-Open Interval
\(\horectl a b\) $\quad:\quad$\horectl a b $\qquad$Half-Open Rectangle (on the left)
\(\horectr c d\) $\quad:\quad$\horectr c d $\qquad$Half-Open Rectangle (on the right)
\(\ideal {a}\) $\quad:\quad$\ideal {a} $\qquad$Ideal of Ring
\(\II\) $\quad:\quad$\II $\qquad$that is: \mathcal I
\(\map \Im z\) $\quad:\quad$\map \Im z $\qquad$Imaginary Part
\(\Img {f}\) $\quad:\quad$\Img {f} $\qquad$Image of Mapping
\(\index {G} {H}\) $\quad:\quad$\index {G} {H} $\qquad$Index of Subgroup
\(\inj\) $\quad:\quad$\inj $\qquad$Canonical Injection
\(\Inn {S}\) $\quad:\quad$\Inn {S} $\qquad$Group of Inner Automorphisms
\(\innerprod {x} {y}\) $\quad:\quad$\innerprod {x} {y} $\qquad$Inner Product
\(\Int {\gamma}\) $\quad:\quad$\Int {\gamma} $\qquad$Interior
\(\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}\) $\quad:\quad$\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a} $\qquad$Limits of Integration
\(\invlaptrans {F}\) $\quad:\quad$\invlaptrans {F} $\qquad$Inverse Laplace Transform
\(\JJ\) $\quad:\quad$\JJ $\qquad$that is: \mathcal J
\(\KK\) $\quad:\quad$\KK $\qquad$that is: \mathcal K
\(\laptrans {f}\) $\quad:\quad$\laptrans {f} $\qquad$Laplace Transform
\(\lcm \set {x, y, z}\) $\quad:\quad$\lcm \set {x, y, z} $\qquad$Lowest Common Multiple
\(\leadstoandfrom\) $\quad:\quad$\leadstoandfrom
\(\leftset {a, b, c}\) $\quad:\quad$\leftset {a, b, c} $\qquad$Conventional set notation (left only)
\(\leftparen {a + b + c}\) $\quad:\quad$\leftparen {a + b + c} $\qquad$Parenthesis (left only)
\(\len {AB}\) $\quad:\quad$\len {AB} $\qquad$Length Function: various
\(\LL\) $\quad:\quad$\LL $\qquad$that is: \mathcal L
\(\Ln\) $\quad:\quad$\Ln $\qquad$Principal Branch of Complex Natural Logarithm
\(\Log\) $\quad:\quad$\Log $\qquad$Principal Branch of Complex Natural Logarithm
\(\map {f} {x}\) $\quad:\quad$\map {f} {x} $\qquad$Mapping or Function
\(\MM\) $\quad:\quad$\MM $\qquad$that is: \mathcal M
\(\Mult\) $\quad:\quad$\Mult $\qquad$Multiplication as a Primitive Recursive Function‎
\(\NegativeBinomial {n} {p}\) $\quad:\quad$\NegativeBinomial {n} {p} $\qquad$Negative Binomial Distribution
\(\Nil {R}\) $\quad:\quad$\Nil {R} $\qquad$Nilradical of Ring
\(\nint {11.98}\) $\quad:\quad$\nint {11.98} $\qquad$Nearest Integer Function
\(\NN\) $\quad:\quad$\NN $\qquad$that is: \mathcal N
\(\norm {z^2}\) $\quad:\quad$\norm {z^2} $\qquad$Norm
\(\O\) $\quad:\quad$\O $\qquad$Empty Set
\(\OO\) $\quad:\quad$\OO $\qquad$that is: \mathcal O
\(\oldpence\) $\quad:\quad$\oldpence $\qquad$old pence
\(\On\) $\quad:\quad$\On $\qquad$Ordinal Class
\(\openint {a} {b}\) $\quad:\quad$\openint {a} {b} $\qquad$Open Interval
\(\Orb S\) $\quad:\quad$\Orb S $\qquad$Orbit
\(\Ord {S}\) $\quad:\quad$\Ord {S} $\qquad$$S$ is an Ordinal
\(\order {G}\) $\quad:\quad$\order {G} $\qquad$Order of Structure, and so on
\(\ot\) $\quad:\quad$\ot $\qquad$Order Type
\(\Out {G}\) $\quad:\quad$\Out {G} $\qquad$Group of Outer Automorphisms
\(\paren {a + b + c}\) $\quad:\quad$\paren {a + b + c} $\qquad$Parenthesis
\(\Poisson {\lambda}\) $\quad:\quad$\Poisson {\lambda} $\qquad$Poisson Distribution
\(\polar {r, \theta}\) $\quad:\quad$\polar {r, \theta} $\qquad$Polar Form of Complex Number
\(\pounds\) $\quad:\quad$\pounds $\qquad$Pound Sterling
\(\powerset {S}\) $\quad:\quad$\powerset {S} $\qquad$Power Set
\(\PP\) $\quad:\quad$\PP $\qquad$that is: \mathcal P
\(\map {\pr_j} {F}\) $\quad:\quad$\map {\pr_j} {F} $\qquad$Projection
\(\Preimg {f}\) $\quad:\quad$\Preimg {f} $\qquad$Preimage of Mapping
\(\map {\proj_\mathbf v} {\mathbf u}\) $\quad:\quad$\map {\proj_\mathbf v} {\mathbf u} $\qquad$Vector Projection
\(\PV\) $\quad:\quad$\PV $\qquad$Cauchy Principal Value
\(\QQ\) $\quad:\quad$\QQ $\qquad$that is: \mathcal Q
\(\radians\) $\quad:\quad$\radians $\qquad$Radian
\(\Rad\) $\quad:\quad$\Rad $\qquad$Radical of Ideal of Ring
\(\ds \int \map f x \rd x\) $\quad:\quad$\ds \int \map f x \rd x $\qquad$Roman $\d$ for use in Integrals
\(\rD\) $\quad:\quad$\rD $\qquad$Differential Operator
\(y \rdelta x\) $\quad:\quad$y \rdelta x $\qquad$$\delta$ operator for use in sums
\(\map \Re z\) $\quad:\quad$\map \Re z $\qquad$Real Part
\(\relcomp {S} {A}\) $\quad:\quad$\relcomp {S} {A} $\qquad$Relative Complement
\(\rem\) $\quad:\quad$\rem $\qquad$Remainder
\(\Res {f} {z_0}\) $\quad:\quad$\Res {f} {z_0} $\qquad$Residue
\(\rightparen {a + b + c}\) $\quad:\quad$\rightparen {a + b + c} $\qquad$Parenthesis (right only)
\(\rightset {a, b, c}\) $\quad:\quad$\rightset {a, b, c} $\qquad$Conventional set notation (right only)
\(\Rng {f}\) $\quad:\quad$\Rng {f} $\qquad$Range of Mapping
\(\RR\) $\quad:\quad$\RR $\qquad$that is: \mathcal R
\(\sech\) $\quad:\quad$\sech $\qquad$Hyperbolic Secant
\(\Sech\) $\quad:\quad$\Sech $\qquad$Hyperbolic Secant
\(\sequence {a_n}\) $\quad:\quad$\sequence {a_n} $\qquad$Sequence
\(\set {a, b, c}\) $\quad:\quad$\set {a, b, c} $\qquad$Conventional set notation
\(\ShiftedGeometric {p}\) $\quad:\quad$\ShiftedGeometric {p} $\qquad$Shifted Geometric Distribution
\(\shillings\) $\quad:\quad$\shillings $\qquad$shillings
\(\Si\) $\quad:\quad$\Si $\qquad$Sine Integral Function
\(\Sinh\) $\quad:\quad$\Sinh $\qquad$Hyperbolic Sine
\(\size {x}\) $\quad:\quad$\size {x} $\qquad$Absolute Value, and so on
\(\SL {n, \R}\) $\quad:\quad$\SL {n, \R} $\qquad$Special Linear Group
\(\span\) $\quad:\quad$\span $\qquad$Linear Span
\(\Spec {R}\) $\quad:\quad$\Spec {R} $\qquad$Spectrum of Ring
\(\sqbrk {a} \) $\quad:\quad$\sqbrk {a}
\(\SS\) $\quad:\quad$\SS $\qquad$that is: \mathcal S
\(\Stab x\) $\quad:\quad$\Stab x $\qquad$Stabilizer
\(\stratgame {N} {A_i} {\succsim_i}\) $\quad:\quad$\stratgame {N} {A_i} {\succsim_i} $\qquad$Strategic Game
\(\struct {G, \circ}\) $\quad:\quad$\struct {G, \circ} $\qquad$Algebraic Structure
\(\StudentT {k}\) $\quad:\quad$\StudentT {k} $\qquad$Student's t-Distribution
\(\SU {n}\) $\quad:\quad$\SU {n} $\qquad$Unimodular Unitary Group
\(\Succ\) $\quad:\quad$\Succ $\qquad$Successor Function
\(\supp\) $\quad:\quad$\supp $\qquad$Support
\(\Syl {p} {N}\) $\quad:\quad$\Syl {p} {N} $\qquad$Sylow $p$-Subgroup
\(\symdif\) $\quad:\quad$\symdif $\qquad$Symmetric Difference
\(\T\) $\quad:\quad$\T $\qquad$True
\(\Tanh\) $\quad:\quad$\Tanh $\qquad$Hyperbolic Tangent
\(\tr\) $\quad:\quad$\tr $\qquad$Trace
\(\TT\) $\quad:\quad$\TT $\qquad$that is: \mathcal T
\(\tuple {a, b, c}\) $\quad:\quad$\tuple {a, b, c} $\qquad$Ordered Tuple
\(\UU\) $\quad:\quad$\UU $\qquad$that is: \mathcal U
\(\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi} \) $\quad:\quad$\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi}
\(\var {X}\) $\quad:\quad$\var {X} $\qquad$Variance
\(\vers \theta\) $\quad:\quad$\vers \theta $\qquad$Versed Sine
\(\VV\) $\quad:\quad$\VV $\qquad$that is: \mathcal V
\(\WW\) $\quad:\quad$\WW $\qquad$that is: \mathcal W
\(\XX\) $\quad:\quad$\XX $\qquad$that is: \mathcal X
\(\YY\) $\quad:\quad$\YY $\qquad$that is: \mathcal Y
\(\ZZ\) $\quad:\quad$\ZZ $\qquad$that is: \mathcal Z


A thing or two

I thought I'd dump some ideas here since my activity may wane a bit over the next few months and I might as well say these things while they're fresh. (then I'll have exams late April-mid June, after that I'll resume to current levels with another semester's knowledge) First I wanted to say that I'm planning on maintaining the page User:Caliburn/Job List as well as I can. The intention is for new contributors to be able to come along and find what still needs working on and gaps that people may not have noticed. Also a handy list for myself so I know what still needs to be done. People are free to add to the list or take off stuff they've completed. I am not sure where to put it for maximum visibility, but I'll display it on my userpage and post it here.

There are already a number of contributors who have their own way of managing their to-do lists, but a global one may have a use. I say: go for it, but beware that it's just another thing that needs maintenance. There are currently few enough active contributors that this could be extremely useful, especially if they are in the same approximate areas of activity. I can see the points of overlap between measure theory, metric spaces, topology, normed spaces, prob theory, matroid theory etc. etc. where this would be worth applying, in particular. --prime mover (talk) 07:19, 4 January 2022 (UTC)
It seems that I am going to tackle some of your topics simply by following Sasane. Namely, I am almost done with distributions. One thing that has been nagging me is the definition of Dirac delta through limits of various functions. This was one of the main reasons why I decided to work on these topics. However, Sasane does not cover this at all. Hence, after I am done with a couple of exercises, I will briefly switch to a different source (not sure which one) to establish how definitions through limits work out in the distributional sense. Then I will work a bit on the Lebesgue integral and resume where I left off (this can be seen by inspecting hyperlinks in Sasane's book page). Most of the work will be less abstract involving normed vector spaces.--Julius (talk) 12:32, 4 January 2022 (UTC)
I was looking under Category:Distributions so I didn't realise how much you have got through, fair enough. (I think any category containing results about distributions should be a subcategory of this category) Distributions are a huge topic that have only just started getting worked on, so it is probably worth noting as an area to expand anyway. If you need ideas on sources for more work on distributions, the module at Warwick on distributions recommends Friedlander & Joshi's Introduction to the Theory of Distributions, among some Fourier analysis texts by Duoandikoetxea and also by Grafakos. I haven't looked at these myself yet, learning more about distributions is on my "to-do" list for the summer. Wikipedia's page on distributional limits gives an example of a sequence of functions converging in the distributional sense to $\pi \delta_0$ (not sure if it's the canonical one, if there is one) so that might also be a good jumping off point. Looking forward to seeing how it all turns out. Caliburn (talk) 15:50, 4 January 2022 (UTC)

Second I'm wondering how theorems could be catalogued so that they don't get lost. While having a descriptive name for each theorem makes the most sense, it can make navigation difficult since some pages have to be given unintuitive names, some more so than others. (sometimes leading to mistakenly duplicate pages) I like pages like Properties of Beta Function for this purpose. I'm wondering whether we could branch this out to have easily navigable collections of other results. No specific format to mind yet. My contribution backlog at the moment is massive, so I doubt I will get to this soon, (especially as it's a significant undertaking) I will return to this idea when it's been whittled down a bit. Caliburn (talk) 00:19, 4 January 2022 (UTC)

I too am a fan of the "Properties of ..." sort of page. The archetype is Subset Equivalences, which I have found very useful indeed.
While duplicate pages are a problem, it's not a serious one. It happens for minor stepping-stone results when multiple source are being used to flesh out an area -- but when we implement categories more incisively, these duplicates are usually caught. The problem mainly happens when a contributor puts every result in a high-level all-inclusive category called, e.g. "Real Analysis" or "Metric Spaces", then it's easier to miss stuff.
Best advice while an area is being fleshed out is: if you see a potential duplication, slap a template in there to flag it up and move on with what you're doing, then after all is in place, take a step back to see whether there is a common thread that would need to be refactored out. --prime mover (talk) 07:19, 4 January 2022 (UTC)
I think once measure theory is fleshed out I'll have pages like "Limit Theorems for (Riemann/etc.) Integrals" and "Properties of Measures", etc. As an aside - should we archive a few older discussions here? My browser is starting to lag a bit typing this response. Caliburn (talk) 15:50, 4 January 2022 (UTC)
Aside -- job done. Good call. --prime mover (talk) 17:16, 4 January 2022 (UTC)

Slow

I don't want to be irritating, but the site has been extremely slow on and off for the past few days. Could this be looked in to? It is making refactoring very sluggish. Caliburn (talk) 18:44, 18 January 2022 (UTC)

Haven't noticed it myself. I do hope I'm not the problem. --prime mover (talk) 20:23, 18 January 2022 (UTC)
Doesn't seem like it, happens on and off even if I'm the only one editing. Doesn't seem as bad right now. Caliburn (talk) 19:13, 19 January 2022 (UTC)