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that to find an infimum, one must know a set and a subset that you want to find the infimum of? And in what cases would the infimum *not* belong to the...
Click to read more »Essential supremum and essential infimum → Essential infimum and essential supremum – For consistency with Infimum and supremum. This is both the alphabetical...
Click to read more »What is meant is that there is one, perhaps + or - infinity. See also infimum, where I added a phrase to clarify, we can do that here also. - Patrick...
Click to read more »supremum and an infimum;'. This does not state that a non-empty subset bounded above (but not below) has a supremum, and likewise for infimum. This is to...
Click to read more »definition of modulus of convexity to the form more commonly used, where the infimum is taken over pairs of points in the unit _sphere_ and not the unit _ball_...
Click to read more »electromagnetic-material, optic-material, philosophy-material(materialism), add infimum...sorry forgot my password again...75.82.19.242 (talk) 19:19, 18 June 2022...
Click to read more »order to be more precise in terminology, I believe it should refer to the infimum instead of the minimum, but I would like to better know the motivations...
Click to read more »Even if Y is a single point and f is linear in x, it need not reach its infimum on a non-compact X. Boris Tsirelson (talk) 07:14, 15 May 2017 (UTC)...
Click to read more »(UTC) isn't it slightly misleading to say that the initial ordinal is the infimum of a set of ordinals? wouldn't it be more appropriate to place a minimum...
Click to read more »satisfying the condition. Is Linnik's constant the smallest L? Or possibly the infimum of the L values if there is no smallest? Or is Linnik's constant not a...
Click to read more »of R ¯ {\displaystyle {\overline {\mathbb {R} }}} has both supremum and infimum". Therefore, this revert was inappropriate. Ladislav Mecir (talk) 16:34...
Click to read more »slightly rewrite the article to emphasize "lower envelope"/"pointwise infimum" of a family of functions, and then mention the special case of a finite...
Click to read more »s = 0. Taking the juxtaposition to mean a quotient, it means that the infimum is ∞, i.e. the set is empty. BTW the proof is too long and complicated...
Click to read more »its maximal/minimal element.", what's the point of that? supremum and infimum are stronger 192.76.172.10 (talk) 17:47, 16 May 2014 (UTC) It seems that...
Click to read more »minimal elements – I like to conform these pages to the title style of Infimum and supremum (i.e., greatest lower bound and least upper bound). At any...
Click to read more »an interval contained in R). Then, its oscillation is: supremum(f(I))-infimum(f(I)). 46.19.85.55 (talk) 18:39, 10 August 2014 (UTC) merge? Fgnievinski...
Click to read more »infimum of the sum of radii of etc... but when taking the measure of a set, one must fix an upper bound on the possible radii, then take the infimum,...
Click to read more »the set of elements with a succsesor is definable, and is Z. This has no infimum. Thehalfone 12:58, 11 June 2007 (UTC) I would guess the original author...
Click to read more »inferior and limit superior are more general terms that represent the infimum and supremum (respectively) of all limit points of a set. The limit inferior...
Click to read more »defines the distance between two sets, and mixes two distances. One is the infimum of distances between 2 points, which is zero, if two sets have a common...
Click to read more »final topology on X with respect to the functions idX : (X, τi) → X is the infimum (or meet) of the topologies {τi} in the lattice of topologies on X. That...
Click to read more »thus well-ordered. The infimum of any nonempty subclass of a well-ordered class exists and is a member of the subclass. So "infimum" and "minimum" mean the...
Click to read more »2007 (UTC) Thank you Lavaka 18:51, 10 January 2007 (UTC) ...where the infimum suprenum is over all 1-Lipschitz functions... —Preceding unsigned comment...
Click to read more »ak is in a subgroup of S for some k. Every nonempty subset of E has an infimum. Every subgroup of S is trivial. It isn't clear whether these are intended...
Click to read more »infimum is attained also for x=-1, so arg inf f(x) = {-1, 1}. Isheden (talk) 11:56, 19 July 2011 (UTC) I just discovered that inf stands for infimum,...
Click to read more »following WikiProjects: Beetles Low‑importance Insects portal Ctenostoma infimum is within the scope of WikiProject Beetles, an attempt to better organize...
Click to read more »18 April 2023 (UTC) I think that it worth to explicitly note that the infimum in ‖ [ x ] ‖ X / M = inf m ∈ M ‖ x − m ‖ X . {\displaystyle \|[x]\|_{X/M}=\inf...
Click to read more »the partial order. A poset need not have a smallest element, but it can. Infimum or meet are other common words used in partial orders and lattices. The...
Click to read more »{\displaystyle \inf _{x\in R\setminus \{0\}}} mean? I know that it's the infimum, but would a casual reader? If the article isn't meant for casual readers...
Click to read more »your recent edit is better. I had some concern about the use of the term infimum, but concluded that readers not familiar with it would also be unfamiliar...
Click to read more »sets of a topological space need not be open, such a family DOES have an infimum in the open set lattice, which is the interior of its intersection. --fudo...
Click to read more »problematic: First of all to make the two definitions (limit vs infimum) agree, the infimum must be restricted to θ > 0 {\displaystyle \theta >0} . Second...
Click to read more »s_{n}} is negative, but they are expected to be increasing because they are infimum of a set which become smaller and smaller since N n {\displaystyle N_{n}}...
Click to read more »not the same as Minkowski dimension. Packing dimension of a set A is the infimum of all numbers s for which P(A,ε)εs converges to zero where P(A,ε) is the...
Click to read more »divisibility. The supremum is given by the least common multiple and the infimum by the greatest common divisor. What is the least common multiple of an...
Click to read more »is if it has one. The empty set doesn't necessarily have a supremum or infimum. I added it. 173.25.54.191 (talk) 04:44, 26 January 2014 (UTC) Domain theory...
Click to read more »partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known...
Click to read more »on the equivalence classes to be well defined, doesn't it need to be an infimum over the metric distances between all elements of each equivalence class...
Click to read more »come to the definition of the infimum. I thought that the infimum of the class of ordinals was undefined, since an infimum must be a member of the set (or...
Click to read more »limit of s to zero cannot be lower, i.e. why it isn't the case that the infimum is not in the set. I've looked at a few proofs, but I've been unable to...
Click to read more »was surprised when I clicked on the article, and saw that "Existence of infimum and supremum in bounded sets" was listed under "Direct consequences of...
Click to read more »Lebesgue measure is defined as an infimum and saying that it is +∞ can be thought of as meaning that this infimum has no finite bound (potential infinity)...
Click to read more »cumulant-generating function will have vertical asymptote(s) at the infimum of such c, if such an infimum exists etc". Note that x is a negative number here. Something...
Click to read more »}} norm is the essential supremum, see Essential supremum and essential infimum. To see the difference, consider the Kronecker delta function, and see...
Click to read more »{\displaystyle \{\|\mathbf {x} -\mathbf {u} \|\mid \mathbf {u} \in U\}} has an infimum, and due to the completeness of U {\displaystyle U} it is a minimum." Which...
Click to read more »of different formulations? I ask this specifically as the Supremum (or Infimum) formulation is often easier for the non-mathematician to understand. In...
Click to read more »INCORRECT LINK I believe the "Supremum" link is misassociated. It goes to "Infimum" instead of "Supremum". — Preceding unsigned comment added by 67.42.51...
Click to read more »removed, this is only the p=1 case and even then is misleading as the infimum might not be achieved. It should be replaced by a brief explanation of...
Click to read more »\left\{\sum _{i=1}^{\infty }\operatorname {length} (I_{i})\right\}} where the infimum above is taken over all countable covers of A by intervals {Ii}i. Non-measurable...
Click to read more »keep, which won't necessarily be close to their interval's supremum and infimum and so we would need to enclose them in within a sufficiently small interval...
Click to read more »error, one might then try to take a supremum, which would then provide an infimum for the power. But to my knowledge, there is no general accepted convention...
Click to read more »distance between two sets A and B in a metric space as being the minimum (or infimum) of distances between any two points P in A and Q in B. Alternatively,...
Click to read more »number, then the d-dimensional Hausdorff measure Hd(M) is defined to be the infimum of all m > 0 such that for all r > 0, M can be covered by countably many...
Click to read more »(namely 2) is so low as the level achieved by them all (technically their infimum in the poset (Z, |)). So, where's the just patent *wrongness*? And please...
Click to read more »Max (doesn't even link to this article) - Min (links to this article) - Infimum and supremum (no mention of a two argument function) - Greatest element...
Click to read more »definition relies on the completeness axiom and concept of supremum and infimum. If there is another approach to defining a Cauchy sequence I appologize...
Click to read more »{\displaystyle n} floors). Let d ( x , y ) {\displaystyle d(x,y)} be the infimum energy needed to take the machine from state x {\displaystyle x} to state...
Click to read more »else? RMFan1 (talk) 15:36, 2 January 2008 (UTC) No. "inf" and "sup" mean "infimum" and "supremum", respectively. Ralphmerridew (talk) 02:46, 13 March 2008...
Click to read more »This function has none. The image of the function has supremum of 1 and infimum of 0, though (ie. the asymptotes of this function are y=0 and y=1). 82...
Click to read more »greatest such n. However, according to the definition in this article (infimum of the lattice of integers ordered by divisibility), gcd(0,0) is defined...
Click to read more »for comparison, arithmetic operations, and evaluations of supremum and infimum. These definitions are not all from the same source (though presumably...
Click to read more »& Wallman, Munkres, etc. In this simple case, it's enough to take the infimum and supremum to identify the endpoints. For the LCT, there are coloured...
Click to read more »supremum (smallest number no less than all elements of a set), not the infimum (largest number no greater than all elements of a set)? (Not very good...
Click to read more »of all, the convexity definition requires the knowledge of supremum and infimum to find the endpoints, which is usually taught only in (advanced) calculus...
Click to read more »elements, Upper and lower bounds, Greatest element and least element, Infimum and supremum, Initial and terminal objects. Elestrophe (talk) 19:50, 14...
Click to read more »into a metric space by defining the distance between two points as the infimum of the lengths of the paths (continuously differentially curves) connecting...
Click to read more »high school - perhaps before then informally - but I didn't know what "infimum" meant until grad school. That's likely because limits are necessary to...
Click to read more »monotonically increasing (decreasing), and this subsequence has a supremum (infimum) in the interval since the interval is closed and bounded. 208.107.152...
Click to read more »express this precisely by saying that the infimum of the distances between points in A and B is a, but the infimum of the distances between points in A and...
Click to read more »same symbol as logical OR, p∨q; and the greatest lower bound (or meet or infimum) is denoted by same symbol as logical AND, p∧q. The lattice interpretation...
Click to read more »on an open and bounded domain will also be one of the local maxima; the infimum will be one of the local minima--this gives one an easy way to find the...
Click to read more »r − 1 μ ( E k ) {\displaystyle \sum _{k\geq r-1}\mu (E_{k})} , and the infimum is at least ∑ k ≥ r μ ( E k ) {\displaystyle \sum _{k\geq r}\mu (E_{k})}...
Click to read more »entitled Predicate fuzzy logics, where the following is written: ...the infimum (resp. supremum) of the truth degrees... ...what is intended by resp. (an...
Click to read more »is, however, resolvable. It may be noted that in this example 38 is the infimum for the set of dull numbers: while not dull itself, there are no dull numbers...
Click to read more »underlying manifold. First define length of path between points. Then take infimum over all paths connecting points. That gives a distance. Metric tensor...
Click to read more »proof relies on the notion of the limit, or at the least, the supremum and infimum, of areas of polygons. A similar argument also justifies the "triangle...
Click to read more »\liminf _{y\in S_{x}}{\frac {f(y)}{g(y)}}} cannot be a limit inferior but an infimum, inf y ∈ S x f ( y ) g ( y ) {\displaystyle \inf _{y\in S_{x}}{\frac {f(y)}{g(y)}}}...
Click to read more »above exists (and the similar claim about sets bounded from below and infimum). --TedPavlic 15:32, 7 March 2007 (UTC) Additionally, the partition definition...
Click to read more »I wonder if this article needs some rewriting. First, the article starts with a very technical "all operator norm definitions money can buy", which is...
Click to read more »suum unigenitum, consubstantialem sibi, de celi excelso solio misit ad infimum mundi solum, qui preelecte virginis utero sancti Spiritus operatione conceptus...
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