Model: TONKKrongyuth/finetune-all-minilm-I6-v2-proofwiki_w-theorem
Author: TONKKrongyuth
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, tensorboard, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:21701, 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:21701, loss:CosineSimilarityLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: Let $p$ be a [[Definition:Prime Number|prime number]].Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the [[Definition:P-adic Number|$p$-adic numbers]].Let $a \in \Q_p$.For all $\epsilon \in \R_{>0}$, let $\map {B_\epsilon} a$ denote the [[Definition:Open Ball in P-adic Numbers|open $\epsilon$-ball]] of $a$. Then::$\forall n \in Z : \set{\map {B^-_{p^{-m} } } {a + i p^n} : i = 0, \dotsc, p^\paren {m - n} - 1}$ is a [[Definition:Set|set]] of [[Definition:Pairwise Disjoint|pairwise disjoint]] [[Definition:Open Ball of Normed Division Ring|open balls]].
sentences: Let $n \in \Z_{> 0}$ be a [[Definition:Positive Integer|positive integer]].Let $I_n$ be defined as::$\displaystyle I_n = \int_0^{\frac \pi 2} \sin^n x \rd x$Then $\left\langle{I_n}\right\rangle$ is a [[Definition:Decreasing Real Sequence|decreasing sequence of real numbers]] which satisfies::$n I_n = \left({n - 1}\right) I_{n - 2}$Thus::$I_n = \dfrac {n - 1} n  I_{n - 2}$is a [[Definition:Reduction Formula|reduction formula]] for $I_n$., Let $\struct {S, \preceq_1}$ be a [[Definition:Totally Ordered Set|totally ordered set]].Let $\struct {T, \preceq_2}$ be an [[Definition:Ordered Set|ordered set]].Let $\phi: S \to T$ be a [[Definition:Mapping|mapping]].Then $\phi$ is an [[Definition:Order Embedding|order embedding]] {{iff}} $\phi$ is [[Definition:Strictly Increasing Mapping|strictly increasing]].That is::$\forall x, y \in S: x \preceq_1 y \iff \map \phi x \preceq_2 \map \phi y${{iff}}::$\forall x, y \in S: x \prec_1 y \implies \map \phi x \prec_2 \map \phi y$, The [[Definition:Quaternion Group|Quaternion Group]] can be [[Definition:Generator of Group|generated]] by the [[Definition:Square Matrix|matrices]]::$\mathbf a = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}\qquad\mathbf b = \begin{bmatrix} 0 & i \\ i & 0 \end{bmatrix}$where $i$ is the [[Definition:Imaginary Unit|imaginary unit]]::$i^2 = -1$, source_sentence: Let $\psi: S_1 \to S_2$ be defined by::$\forall x \in S_1: \map \psi x = \displaystyle \lim_{n \mathop \to \infty} \map {\psi'} {x_n}$where $x = \displaystyle \lim_{n \mathop \to \infty} x_n$ for some [[Definition:Sequence|sequence]] $\sequence {x_n} \subseteq R_1$Then $\psi$ is a [[Definition:Well-Defined Mapping|well-defined mapping]].
sentences: Let $X$ be a [[Definition:Trivial Topological Space|trivial topological space]].Then $X$ is [[Definition:Indiscrete Space|indiscrete]]., Let $\omega \in A \setminus B$, where $A \setminus B$ denotes the [[Definition:Set Difference|difference]] of $A$ and $B$.Then '''$A$ [[Definition:Occurrence of Event|occurs]] but $B$ does not [[Definition:Occurrence of Event|occur]]'''., === [[Definition:Cosine/Definition from Triangle|Definition from Triangle]] ==={{:Definition:Cosine/Definition from Triangle}}=== [[Definition:Cosine/Definition from Circle|Definition from Circle]] ==={{:Definition:Cosine/Definition from Circle}}=== [[Definition:Cosine/Real Function|Real Numbers]] ==={{:Definition:Cosine/Real Function}}=== [[Definition:Cosine/Complex Function|Complex Numbers]] ==={{:Definition:Cosine/Complex Function}}, source_sentence: Let $S$ be a [[Definition:Finite Set|finite set]].Let $\mathscr B$ be a [[Definition:Non-Empty Set|non-empty]] [[Definition:Set|set]] of [[Definition:Subset|subsets]] of $S$ satisfying the [[Leigh.Samphier/Sandbox/Definition:Base Axiom (Matroid)/Definition 1|base axiom]]:{{:Leigh.Samphier/Sandbox/Definition:Base Axiom (Matroid)/Definition 1}}Then $\mathscr B$ is the set of [[Definition:Base of Matroid|bases]] of a [[Definition:Matroid|matroid]] on $S$.
sentences: Let $M = \struct{S,\mathscr I}$ be an [[Definition:Independence System|independence system]]., Let $F$ be a [[Definition:Subset|subset]] of $S_1$.$f$ '''preserves supremum of''' $F$ {{iff}}:$F$ admits a [[Definition:Supremum of Set|supremum]] in $\left({S_1, \preceq_1}\right)$ implies:: $f^\to \left({F}\right)$ admits a [[Definition:Supremum of Set|supremum]] in $\left({S_2, \preceq_2}\right)$ and $\sup \left({f^\to\left({F}\right)}\right) = f \left({\sup F}\right)$, Let $\sequence {a_n}$ be a [[Definition:Sequence|sequence in $\R$]].If $\displaystyle \lim_{k \mathop \to \infty} a_k \ne 0$, then $\displaystyle \sum_{i \mathop = 1}^\infty a_n$ [[Definition:Divergent Series|diverges]]., source_sentence: Let $\alpha$, $\beta$ and $\gamma$ be [[Definition:Cut (Analysis)|cuts]].Let $\alpha \beta$ denote the [[Definition:Multiplication of Cuts|product]] of $\alpha$ and $\beta$.Then::$\paren {\alpha \beta} \gamma = \alpha \paren {\beta \gamma}$
sentences: Let $m \in \Z$ such that $m > 1$.The '''additive group of integers modulo $m$''' $\struct {\Z_m, +_m}$ is the [[Definition:Set|set]] of [[Definition:Integers Modulo m|integers modulo $m$]] under the [[Definition:Binary Operation|operation]] of [[Definition:Modulo Addition|addition modulo $m$]]., Let $\left({S, \mathcal R}\right)$ be a [[Definition:Relational Structure|relational structure]], that is, a [[Definition:Set|set]] $S$ endowed with a [[Definition:Endorelation|binary relation]] $\mathcal R$.Let $T \subseteq S$ be a [[Definition:Subset|subset]] of $S$.Then $T$ is a '''cofinal subset of $S$ with respect to $\mathcal R$''' {{iff}}::$\forall x \in S: \exists t \in T: x \mathop {\mathcal R} t$, A '''Diophantine equation''' is an [[Definition:Indeterminate Equation|indeterminate]] [[Definition:Polynomial Equation|polynomial equation]] that allows the variables to take [[Definition:Integer|integer]] values only., source_sentence: Let $m$ be a [[Definition:Number|numbers]] which is presented to $d$ [[Definition:Significant Figures|significant figures]].Then the most [[Definition:Significant Figures|significant figures]] that $\sqrt m$ can have is also $d$.
sentences: :$\displaystyle \int x \csc a x \rd x = \frac 1 {a^2} \paren {a x + \frac {\paren {a x}^3} {18} + \frac {7 \paren {a x}^5} {1800} + \cdots + \frac {\paren {-1}^{n - 1} 2 \paren {2^{2 n - 1} - 1} B_n \paren {a x}^{2 n + 1} } {\paren {2 n + 1}!} + \cdots} + C$where $B_{2 n}$ is the $2 n$th [[Definition:Bernoulli Numbers|Bernoulli number]]., === [[Definition:Golden Mean/Definition 1|Definition 1]] ==={{:Definition:Golden Mean/Definition 1}}=== [[Definition:Golden Mean/Definition 2|Definition 2]] ==={{:Definition:Golden Mean/Definition 2}}, Let $G$ be a [[Definition:Group|group]].Let $N$ be a [[Definition:Subgroup|subgroup]] of $G$.$N$ is a '''normal subgroup of $G$''' {{iff}}:=== [[Definition:Normal Subgroup/Definition 1|Definition 1]] ==={{:Definition:Normal Subgroup/Definition 1}}=== [[Definition:Normal Subgroup/Definition 2|Definition 2]] ==={{:Definition:Normal Subgroup/Definition 2}}=== [[Definition:Normal Subgroup/Definition 3|Definition 3]] ==={{:Definition:Normal Subgroup/Definition 3}}=== [[Definition:Normal Subgroup/Definition 4|Definition 4]] ==={{:Definition:Normal Subgroup/Definition 4}}=== [[Definition:Normal Subgroup/Definition 5|Definition 5]] ==={{:Definition:Normal Subgroup/Definition 5}}=== [[Definition:Normal Subgroup/Definition 6|Definition 6]] ==={{:Definition:Normal Subgroup/Definition 6}}=== [[Definition:Normal Subgroup/Definition 7|Definition 7]] ==={{:Definition:Normal Subgroup/Definition 7}}
pipeline_tag: sentence-similarity
library_name: sentence-transformers
Likes: 0 | All-time downloads: 13
Created: 2025-02-17 12:31:37