Model: TONKKrongyuth/finetune-all-minilm-L6-v2-proofwiki_wo-theorem
Author: TONKKrongyuth
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, tensorboard, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:20935, loss:CosineSimilarityLoss, arxiv:1908.10084, base_model:sentence-transformers/all-MiniLM-L6-v2, base_model:finetune:sentence-transformers/all-MiniLM-L6-v2, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: sentence-transformers/all-MiniLM-L6-v2
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:20935, loss:CosineSimilarityLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: Let $B$ be a [[Definition:Base of Matroid|base]] of $M$.Let $x \in S \setminus B$.Then there exists a unique [[Definition:Circuit|circuit]] $C$ such that::$x \in C \subseteq B \cup \set x$That is, $C$ is the [[Definition:Fundamental Circuit (Matroid)|fundamental circuit]] of $x$ in $B$.
sentences: Let $r \in \R_{>0}$.For $n \in \N_{> 0}$ the '''Harmonic numbers order $r$''' are defined as follows::$\displaystyle H_n^{\paren r} = \sum_{k \mathop = 1}^n \frac 1 {k^r}$, $m$ and $n$ are '''quasiamicable numbers''' {{iff}}::$\sigma \left({m}\right) = \sigma \left({n}\right) = m + n + 1$where $\sigma \left({m}\right)$ denotes the [[Definition:Sigma Function|$\sigma$ function]]., The '''lunar month''' is defined as the [[Definition:Length of Time|length of time]] between $2$ [[Definition:New Moon|new moons]].:$1$ '''lunar month''' $\approx 29 \cdotp 530588$ [[Definition:Day|days]]or::$1$ '''lunar month''' $\approx 29$ [[Definition:Day|days]], $12$ [[Definition:Hour|hours]], $44$ [[Definition:Minute of Time|minutes]] and $2 \cdotp 8$ [[Definition:Second of Time|seconds]]., source_sentence: Let $p$ be a [[Definition:Prime Number|prime number]].Let $G$ be a [[Definition:Group|group]] of [[Definition:Order of Group|order]] $p$.Let $\Aut G$ denote the [[Definition:Automorphism Group|automorphism group]] of $G$.Then::$\order {\Aut G} = p - 1$where $\order {\, \cdot \,}$ denotes the [[Definition:Order of Group|order]] of a [[Definition:Group|group]].
sentences: Let $\alpha$ be a [[Definition:Cut (Analysis)|cut]].Let $q \in \Q$ such that $q \notin \alpha$.Then $p$ is referred to as an '''upper number''' of $\alpha$., A '''group''' is a [[Definition:Semigroup|semigroup]] with an [[Definition:Identity Element|identity]] (that is, a [[Definition:Monoid|monoid]]) in which every [[Definition:Element|element]] has an [[Definition:Inverse Element|inverse]]., The '''strictly positive integers''' are the set defined as::$\Z_{> 0} := \set {x \in \Z: x > 0}$That is, all the [[Definition:Integer|integers]] that are strictly greater than [[Definition:Zero (Number)|zero]]::$\Z_{> 0} := \set {1, 2, 3, \ldots}$, source_sentence: :$f + g: \struct {S, \tau_{_S} } \to \struct {R, \tau_{_R} }$ is [[Definition:Continuous Mapping on Set|continuous]].
sentences: Let $S$ be a [[Definition:Set|set]].Let $\circ : S \times S \to S$ be a [[Definition:Binary Operation|binary operation]].Then $\circ$ is '''associative''' {{iff}}::$\forall x, y, z \in S: \paren {x \circ y} \circ z = x \circ \paren {y \circ z}$, Let $S$ be a [[Definition:Subset|subset]] of $S_1$.The mapping $f$ is '''continuous on $S$''' {{iff}} $f$ is [[Definition:Continuous Mapping at Point (Topology)|continuous at every point]] $x \in S$., The [[Definition:Vertical Circle|vertical circle]] on the [[Definition:Celestial Sphere|celestial sphere]] which passes through both the [[Definition:East Point of Horizon|east point]] and the [[Definition:West Point of Horizon|west point]] is called the '''prime vertical'''., source_sentence: Let $c$ be a [[Definition:Number|number]].Let $\left\langle{b_n}\right\rangle$ be the [[Definition:Sequence|sequence]] defined as::$b_n = \begin{cases}0 & : n = 0 \\1 & : n = 1 \\b_{n - 2} + b_{n - 1} + c & : n > 1\end{cases}$Then $\left\langle{b_n}\right\rangle$  can be expressed in [[Definition:Fibonacci Number|Fibonacci numbers]] as::$b_n = c F_{n - 1} + \left({c + 1}\right) F_n - c$
sentences: Let $T = \struct {S, \tau}$ be a [[Definition:Topological Space|topological space]].Let $A \subseteq S$.=== [[Definition:Adherent Point/Definition 3|Definition from Neighborhood]] ==={{:Definition:Adherent Point/Definition 3}}=== [[Definition:Adherent Point/Definition 1|Definition from Open Neighborhood]] ==={{:Definition:Adherent Point/Definition 1}}=== [[Definition:Adherent Point/Definition 2|Definition from Closure]] ==={{:Definition:Adherent Point/Definition 2}}, $\RR$ is '''transitive''' {{iff}}::$\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$that is::$\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \in \RR$, The '''Fibonacci numbers''' are a [[Definition:Sequence|sequence]] $\sequence {F_n}$ of [[Definition:Integer|integers]] which is formally defined recursively as::$F_n = \begin {cases} 0 & : n = 0 \\1 & : n = 1 \\F_{n - 1} + F_{n - 2} & : \text {otherwise} \end {cases}$for all $n \in \Z_{\ge 0}$., source_sentence: :$\displaystyle \sum_{n \mathop = 1}^\infty \dfrac 1 {x_n \map {J_0 } {x_n} } = 0 \cdotp 38479 \ldots$where::$x_n$ is the $n$th [[Definition:Zero of Function|zero]] of the [[Definition:Bessel Function of the First Kind|order $1$ Bessel function of the first kind]]:$\map {J_0 } {x_n}$ is the [[Definition:Bessel Function of the First Kind|order $0$ Bessel function of the first kind]] of $x_n$.
sentences: Let $\tuple {q_1, q_2, q_3}$ denote a set of [[Definition:Curvilinear Coordinate System|curvilinear coordinates]].Let the relation between those [[Definition:Curvilinear Coordinate System|curvilinear coordinates]] and [[Definition:Cartesian Coordinates|Cartesian coordinates]] be expressed as:{{begin-eqn}}{{eqn | l = x      | r = \map x {q_1, q_2, q_3}}}{{eqn | l = y      | r = \map y {q_1, q_2, q_3}}}{{eqn | l = z      | r = \map z {q_1, q_2, q_3}}}{{end-eqn}}where $\tuple {x, y, z}$ denotes the [[Definition:Cartesian Coordinates|Cartesian coordinates]].Let these equations have the property that::$\dfrac {\partial x} {\partial q_i} \dfrac {\partial x} {\partial q_j} + \dfrac {\partial y} {\partial q_i} \dfrac {\partial y} {\partial q_j} + \dfrac {\partial z} {\partial q_i} \dfrac {\partial z} {\partial q_j} = 0$wherever $i \ne j$.Then $\tuple {q_1, q_2, q_3}$ are '''orthogonal curvilinear coordinates'''., === [[Definition:Prime Number/Definition 1|Definition 1]] ==={{:Definition:Prime Number/Definition 1}}=== [[Definition:Prime Number/Definition 2|Definition 2]] ==={{:Definition:Prime Number/Definition 2}}=== [[Definition:Prime Number/Definition 3|Definition 3]] ==={{:Definition:Prime Number/Definition 3}}=== [[Definition:Prime Number/Definition 4|Definition 4]] ==={{:Definition:Prime Number/Definition 4}}=== [[Definition:Prime Number/Definition 5|Definition 5]] ==={{:Definition:Prime Number/Definition 5}}=== [[Definition:Prime Number/Definition 6|Definition 6]] ==={{:Definition:Prime Number/Definition 6}}=== [[Definition:Prime Number/Definition 7|Definition 7]] ==={{:Definition:Prime Number/Definition 7}}=== Euclid's Definition ==={{EuclidSaid}}:''{{:Definition:Euclid's Definitions - Book VII/11 - Prime Number}}''{{EuclidDefRefNocat|VII|11|Prime Number}}, A '''Bessel function of the first kind of order $n$''' is a [[Definition:Bessel Function|Bessel function]] which is [[Definition:Non-Singular Point|non-singular]] at the [[Definition:Origin|origin]]It is usually denoted $\map {J_n} x$, where $x$ is the [[Definition:Dependent Variable|dependent variable]] of the instance of '''[[Definition:Bessel's Equation|Bessel's equation]]''' to which $\map {J_n} x$ forms a [[Definition:Solution of Differential Equation|solution]].
pipeline_tag: sentence-similarity
library_name: sentence-transformers
Likes: 0 | All-time downloads: 118
Created: 2025-02-19 05:37:06