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tautological

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tautological
tautological, a. (tɔːtəʊˈlɒdʒɪkəl) [f. as prec. + -al1: see -ical.] 1. a. Pertaining to, characterized by, involving, or using tautology; repeating the same word, or the same notion in different words.1620 T. Granger Div. Logike 387 Lest thy discourse be tedious, Tautologicall, erroneous. 1670 Bloun... Oxford English Dictionary
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Tautological
In mathematics, tautological may refer to: Logic: Tautological consequence Geometry, where it is used as an alternative to canonical: Tautological bundle Tautological line bundle Tautological one-form Tautology (grammar), unnecessary repetition, or more words than necessary, to say the same thing. wikipedia.org
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tautological
tautological/ˌtɔ:təˈlɔdʒɪkl; ˌtɔtl`ɑdʒɪkl/, tautologous / tɔ:ˈtɔləgəs; tɔ`tɑləɡəs/ adjs. 牛津英汉双解词典
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Tautological one-form
is preferred, as in tautological bundle. Properties The tautological one-form is the unique one-form that "cancels" pullback. wikipedia.org
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Tautological bundle
In the case of projective space the tautological bundle is known as the tautological line bundle. If has dimension , the tautological line bundle is one tautological bundle, and the other, just described, is of rank . wikipedia.org
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Definition of tautological action What is the precise meaning of the term 'tautological action' as used for example in this Wikipedia page in the context of semigroup actions? For reference the particular sentence is...
The tautological action is this action.
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Tautological ring
In algebraic geometry, the tautological ring is the subring of the Chow ring of the moduli space of curves generated by tautological classes. As of 2016, it is not known whether the tautological and tautological cohomology rings are isomorphic. wikipedia.org
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why is the tautological one-form called the canonical one-form?
In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle of a manifold.
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Tautological consequence
Not all logical consequences are tautological consequences. Reviewing the truth table, it turns out the conclusion of the argument is not a tautological consequence of the premise. wikipedia.org
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disjunct set D is tautological $\iff$ D contains both p and $\neg p$ We say that a set of literals D has model the interpretation I, if which there's a literal p in D, s.t. $I \models p$. D is tautological if every in...
Thus, for every $I$ we have that $I \vDash D$, and this means that $D$ is tautological. We have $I \nvDash D$, contradicting the fact that $D$ is tautological.
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List of tautological place names
A place name is tautological if two differently sounding parts of it are synonymous. Thus, for example, New Zealand's Mount Maunganui is tautological since "maunganui" is Māori for "great mountain". wikipedia.org
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Projectivizations of Tautological bundles Let $Gr(k,n)$ be the Grassmannian of $k$-planes, and $Q$ its tautological quotient bundle. Is there a nice description of the projective bundle $P(Q)$ associated to $Q$? Is it...
Of course, it is not a Grassmannian (for instance, by the reason mentioned by Mohan), but it is a (partial) flag variety --- either $Fl(k,k+1;n)$ or $Fl(k,n-1;n)$, depending on which convention for $P(Q)$ is used.
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Discrete Mathematics proving tautological implications argument proof ...
Argument Form DEFINITION An argument form(论证形式) is a sequence of formulas • Valid: no matter which propositions are substituted for the propositional variables, the truth of conclusion follows from the truth of premises • rules of inference(推理规则): valid argument forms EXAMPLE: a valid argument form and an invalid argument form valid invalid
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Tautological vector bundle over $G_1(\mathbb{R^2})$ isomorphic to the Möbius bundle > Let $V$ be a finite dimensional vector space, and let $G_k(V)$ be the Grassmannian of $k$-dimensional subspaces of $V$. Let $T$ be ...
As @Sam pointed out $G_1(\mathbb{R^2}) \cong \mathbb{RP^1} \cong \mathbb{S^1}$. Now, writing a smooth bundle isomorphism is not so hard.
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Logic: Proving tautological consequence I'm having trouble proving this tautological consequence. I'd hope that you guys can maybe oversee my process and identify errors, because I went over this couple of times and I...
make a truth table of $$((a \rightarrow b) \land (c \rightarrow b)) \rightarrow ((a \lor c) \rightarrow b)$$ instead.
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