ill defined mathematics

If the construction was well-defined on its own, what would be the point of AoI? Document the agreement(s). Gestalt psychologists find it is important to think of problems as a whole. Below is a list of ill defined words - that is, words related to ill defined. Is there a detailed definition of the concept of a 'variable', and why do we use them as such? p\in \omega\ s.t\ m+p=n$, Using Replacement to prove transitive closure is a set without recursion. This paper describes a specific ill-defined problem that was successfully used as an assignment in a recent CS1 course. The idea of conditional well-posedness was also found by B.L. Lavrent'ev, V.G. Various physical and technological questions lead to the problems listed (see [TiAr]). A second question is: What algorithms are there for the construction of such solutions? If we want $w=\omega_0$ then we have to specify that there can only be finitely many $+$ above $0$. ill deeds. Nonlinear algorithms include the . Tip Two: Make a statement about your issue. Disequilibration for Teaching the Scientific Method in Computer Science. A function that is not well-defined, is actually not even a function. How to match a specific column position till the end of line? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. It identifies the difference between a process or products current (problem) and desired (goal) state. \label{eq2} Proof of "a set is in V iff it's pure and well-founded". A number of problems important in practice leads to the minimization of functionals $f[z]$. Consider the "function" $f: a/b \mapsto (a+1)/b$. ($F_1$ can be the whole of $Z$.) This set is unique, by the Axiom of Extensionality, and is the set of the natural numbers, which we represent by $\mathbb{N}$. For convenience, I copy parts of the question here: For a set $A$, we define $A^+:=A\cup\{A\}$. We've added a "Necessary cookies only" option to the cookie consent popup, For $m,n\in \omega, m \leq n$ imply $\exists ! You missed the opportunity to title this question 'Is "well defined" well defined? Furthermore, competing factors may suggest several approaches to the problem, requiring careful analysis to determine the best approach. You have to figure all that out for yourself. But we also must make sure that the choice of $c$ is irrelevant, that is: Whenever $g(c)=g(c')$ it must also be true that $h(c)=h(c')$. al restrictions on $\Omega[z] $ (quasi-monotonicity of $\Omega[z]$, see [TiAr]) it can be proved that $\inf\Omega[z]$ is attained on elements $z_\delta$ for which $\rho_U(Az_\delta,u_\delta) = \delta$. If there is an $\alpha$ for which $\rho_U(Az_\alpha,u_\delta) = \delta$, then the original variational problem is equivalent to that of minimizing $M^\alpha[z,u_\delta]$, which can be solved by various methods on a computer (for example, by solving the corresponding Euler equation for $M^\alpha[z,u_\delta]$). The use of ill-defined problems for developing problem-solving and Under these conditions one cannot take, following classical ideas, an exact solution of \ref{eq2}, that is, the element $z=A^{-1}\tilde{u}$, as an approximate "solution" to $z_T$. Most common presentation: ill-defined osteolytic lesion with multiple small holes in the diaphysis of a long bone in a child with a large soft tissue mass. Delivered to your inbox! How can I say the phrase "only finitely many. In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Rather, I mean a problem that is stated in such a way that it is unbounded or poorly bounded by its very nature. If we use infinite or even uncountable . At first glance, this looks kind of ridiculous because we think of $x=y$ as meaning $x$ and $y$ are exactly the same thing, but that is not really how $=$ is used. adjective. soft question - Definition of "well defined" in mathematics 2002 Advanced Placement Computer Science Course Description. Learn how to tell if a set is well defined or not.If you want to view all of my videos in a nicely organized way, please visit https://mathandstatshelp.com/ . This $Z_\delta$ is the set of possible solutions. Proceedings of the 33rd SIGCSE Technical Symposium on Computer Science Education, SIGCSE Bulletin 34(1). ill-defined. Since the 17th century, mathematics has been an indispensable . PROBLEM SOLVING: SIGNIFIKANSI, PENGERTIAN, DAN RAGAMNYA - ResearchGate How to handle a hobby that makes income in US. When we define, Take another set $Y$, and a function $f:X\to Y$. ill-defined, unclear adjective poorly stated or described "he confuses the reader with ill-defined terms and concepts" Wiktionary (0.00 / 0 votes) Rate this definition: ill-defined adjective Poorly defined; blurry, out of focus; lacking a clear boundary. As a pointer, having the axiom of infinity being its own axiom in ZF would be rather silly if this construction was well-defined. [Gr]); for choices of the regularization parameter leading to optimal convergence rates for such methods see [EnGf]. \begin{align} ITS in ill-defined domains: Toward hybrid approaches - Academia.edu However, this point of view, which is natural when applied to certain time-depended phenomena, cannot be extended to all problems. Are there tables of wastage rates for different fruit and veg? By poorly defined, I don't mean a poorly written story. In particular, a function is well-defined if it gives the same result when the form but not the value of an input is changed. Tikhonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. Let $T_{\delta_1}$ be a class of non-negative non-decreasing continuous functions on $[0,\delta_1]$, $z_T$ a solution of \ref{eq1} with right-hand side $u=u_T$, and $A$ a continuous operator from $Z$ to $U$. The term "critical thinking" (CT) is frequently found in educational policy documents in sections outlining curriculum goals. On the basis of these arguments one has formulated the concept (or the condition) of being Tikhonov well-posed, also called conditionally well-posed (see [La]). To save this word, you'll need to log in. Inom matematiken innebr vldefinierad att definitionen av ett uttryck har en unik tolkning eller ger endast ett vrde. Then $R_2(u,\alpha)$ is a regularizing operator for \ref{eq1}. We can then form the quotient $X/E$ (set of all equivalence classes). In this case $A^{-1}$ is continuous on $M$, and if instead of $u_T$ an element $u_\delta$ is known such that $\rho_U(u_\delta,u_T) \leq \delta$ and $u_\delta \in AM$, then as an approximate solution of \ref{eq1} with right-hand side $u = u_\delta$ one can take $z_\delta = A^{-1}u_\delta $. It was last seen in British general knowledge crossword. Well-defined expression - Wikipedia For instance, it is a mental process in psychology and a computerized process in computer science. A variant of this method in Hilbert scales has been developed in [Na] with parameter choice rules given in [Ne]. Why is the set $w={0,1,2,\ldots}$ ill-defined? Ill-Defined -- from Wolfram MathWorld An ill-defined problem is one that addresses complex issues and thus cannot easily be described in a concise, complete manner. June 29, 2022 Posted in&nbspkawasaki monster energy jersey. He is critically (= very badly) ill in hospital. E. C. Gottschalk, Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr., Jr. What is a post and lintel system of construction what problem can occur with a post and lintel system provide an example of an ancient structure that used a post and lintel system? Most businesses arent sufficiently rigorous when developing new products, processes, or even businesses in defining the problems theyre trying to solve and explaining why those issues are critical. - Henry Swanson Feb 1, 2016 at 9:08 For such problems it is irrelevant on what elements the required minimum is attained. In practice the search for $z_\delta$ can be carried out in the following manner: under mild addition An ill-defined problem is one that lacks one or more of the specified properties, and most problems encountered in everyday life fall into this category. So, $f(x)=\sqrt{x}$ is ''well defined'' if we specify, as an example, $f : [0,+\infty) \to \mathbb{R}$ (because in $\mathbb{R}$ the symbol $\sqrt{x}$ is, by definition the positive square root) , but, in the case $ f:\mathbb{R}\to \mathbb{C}$ it is not well defined since it can have two values for the same $x$, and becomes ''well defined'' only if we have some rule for chose one of these values ( e.g. Click the answer to find similar crossword clues . an ill-defined mission. Thence to the Reschen Scheideck Pass the main chain is ill-defined, though on it rises the Corno di Campo (10,844 ft.), beyond which it runs slightly north-east past the sources of the Adda and the Fra g ile Pass, sinks to form the depression of the Ofen Pass, soon bends north and rises once more in the Piz Sesvenna (10,568 ft.). A problem statement is a short description of an issue or a condition that needs to be addressed. Why would this make AoI pointless? Possible solutions must be compared and cross examined, keeping in mind the outcomes which will often vary depending on the methods employed. Lavrent'ev, V.G. The parameter $\alpha$ is determined from the condition $\rho_U(Az_\alpha,u_\delta) = \delta$. Hence we should ask if there exist such function $d.$ We can check that indeed It is critical to understand the vision in order to decide what needs to be done when solving the problem. Learner-Centered Assessment on College Campuses. To do this, we base what we do on axioms : a mathematical argument must use the axioms clearly (with of course the caveat that people with more training are used to various things and so don't need to state the axioms they use, and don't need to go back to very basic levels when they explain their arguments - but that is a question of practice, not principle). Az = u. An expression which is not ambiguous is said to be well-defined . In a physical experiment the quantity $z$ is frequently inaccessible to direct measurement, but what is measured is a certain transform $Az=u$ (also called outcome). Do any two ill-founded models of set theory with order isomorphic ordinals have isomorphic copies of L? $\qquad\qquad\qquad\qquad\qquad\qquad\quad\quad$There exists an inductive set. An example of a function that is well-defined would be the function another set? The numerical parameter $\alpha$ is called the regularization parameter. Now, I will pose the following questions: Was it necessary at all to use any dots, at any point, in the construction of the natural numbers? In other words, we will say that a set $A$ is inductive if: For each $a\in A,\;a\cup\{a\}$ is also an element of $A$. Secondly notice that I used "the" in the definition. Where does this (supposedly) Gibson quote come from? An ill-defined problem is one in which the initial state, goal state, and/or methods are ill-defined. The problem of determining a solution $z=R(u)$ in a metric space $Z$ (with metric $\rho_Z(,)$) from "initial data" $u$ in a metric space $U$ (with metric $\rho_U(,)$) is said to be well-posed on the pair of spaces $(Z,U)$ if: a) for every $u \in U$ there exists a solution $z \in Z$; b) the solution is uniquely determined; and c) the problem is stable on the spaces $(Z,U)$, i.e. We call $y \in \mathbb{R}$ the. Since $\rho_U(Az_T,u_\delta) \leq \delta$, the approximate solution of $Az = u_\delta$ is looked for in the class $Z_\delta$ of elements $z_\delta$ such that $\rho_U(u_\delta,u_T) \leq \delta$. Problem Solving Strategies | Overview, Types & Examples - Video Make it clear what the issue is. If $A$ is a linear operator, $Z$ a Hilbert space and $\Omega[z]$ a strictly-convex functional (for example, quadratic), then the element $z_{\alpha_\delta}$ is unique and $\phi(\alpha)$ is a single-valued function. Problem solving - Wikipedia The real reason it is ill-defined is that it is ill-defined ! We have 6 possible answers in our database. Approximate solutions of badly-conditioned systems can also be found by the regularization method with $\Omega[z] = \norm{z}^2$ (see [TiAr]). Kryanev, "The solution of incorrectly posed problems by methods of successive approximations", M.M. PRINTED FROM OXFORD REFERENCE (www.oxfordreference.com). Tip Two: Make a statement about your issue. The problem statement should be designed to address the Five Ws by focusing on the facts. Under the terms of the licence agreement, an individual user may print out a PDF of a single entry from a reference work in OR for personal use (for details see Privacy Policy and Legal Notice). h = \sup_{\text{$z \in F_1$, $\Omega[z] \neq 0$}} \frac{\rho_U(A_hz,Az)}{\Omega[z]^{1/2}} < \infty. The Tower of Hanoi, the Wason selection task, and water-jar issues are all typical examples. One moose, two moose. Can I tell police to wait and call a lawyer when served with a search warrant? If $A$ is an inductive set, then the sets $\varnothing,\;\{\varnothing\},\;\&\;\{\varnothing,\{\varnothing\}\}$ are all elements of $A$. See also Ambiguous, Ill-Defined , Undefined Explore with Wolfram|Alpha More things to try: partial differential equations ackermann [2,3] exp (z) limit representation Nevertheless, integrated STEM instruction remains ill-defined with many gaps evident in the existing research of how implementation explicitly works. In completing this assignment, students actively participated in the entire process of problem solving and scientific inquiry, from the formulation of a hypothesis, to the design and implementation of experiments (via a program), to the collection and analysis of the experimental data. Therefore this definition is well-defined, i.e., does not depend on a particular choice of circle. Learn more about Stack Overflow the company, and our products. set of natural number $w$ is defined as Despite this frequency, however, precise understandings among teachers of what CT really means are lacking. Let $f(x)$ be a function defined on $\mathbb R^+$ such that $f(x)>0$ and $(f(x))^2=x$, then $f$ is well defined. So the span of the plane would be span (V1,V2). ensures that for the inductive set $A$, there exists a set whose elements are those elements $x$ of $A$ that have the property $P(x)$, or in other words, $\{x\in A|\;P(x)\}$ is a set. No, leave fsolve () aside. il . [a] There is only one possible solution set that fits this description. Problems that are well-defined lead to breakthrough solutions. The exterior derivative on $M$ is a $\mathbb{R}$ linear map $d:\Omega^*(M)\to\Omega^{*+1}(M)$ such that. Two problems arise with this: First of all, we must make sure that for each $a\in A$ there exists $c\in C$ with $g(c)=a$, in other words: $g$ must be surjective. As applied to \ref{eq1}, a problem is said to be conditionally well-posed if it is known that for the exact value of the right-hand side $u=u_T$ there exists a unique solution $z_T$ of \ref{eq1} belonging to a given compact set $M$. Education research has shown that an effective technique for developing problem-solving and critical-thinking skills is to expose students early and often to "ill-defined" problems in their field. NCAA News (2001). Problems for which at least one of the conditions below, which characterize well-posed problems, is violated. &\implies \overline{3x} = \overline{3y} \text{ (In $\mathbb Z_{12}$)}\\ Shishalskii, "Ill-posed problems of mathematical physics and analysis", Amer. After stating this kind of definition we have to be sure that there exist an object with such properties and that the object is unique (or unique up to some isomorphism, see tensor product, free group, product topology). Well-Defined vs. Ill-Defined Problems - alitoiu.com \end{align}. Is there a single-word adjective for "having exceptionally strong moral principles"? But if a set $x$ has the property $P(x)$, then we have that it is an element of every inductive set, and, in particular, is an element of the inductive set $A$, so every natural number belongs to $A$ and: $$\{x\in A|\; P(x)\}=\{x| x\text{ is an element of every inductive set}\}=\{x| x\text{ is a natural number}\}$$, $\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\square$. It is only after youve recognized the source of the problem that you can effectively solve it. Tip Four: Make the most of your Ws.. M^\alpha[z,u_\delta] = \rho_U^2(Az,u_\delta) + \alpha \Omega[z]. \begin{equation} Is a PhD visitor considered as a visiting scholar? What does ill-defined mean? - definitions What exactly is Kirchhoffs name? Compare well-defined problem. As a selection principle for the possible solutions ensuring that one obtains an element (or elements) from $Z_\delta$ depending continuously on $\delta$ and tending to $z_T$ as $\delta \rightarrow 0$, one uses the so-called variational principle (see [Ti]). Can archive.org's Wayback Machine ignore some query terms? Equivalence of the original variational problem with that of finding the minimum of $M^\alpha[z,u_\delta]$ holds, for example, for linear operators $A$. (2000). Personalised Then one might wonder, Can you ship helium balloons in a box? Helium Balloons: How to Blow It Up Using an inflated Mylar balloon, Duranta erecta is a large shrub or small tree. $$ $$ An example that I like is when one tries to define an application on a domain that is a "structure" described by "generators" by assigning a value to the generators and extending to the whole structure. It is critical to understand the vision in order to decide what needs to be done when solving the problem. \abs{f_\delta[z] - f[z]} \leq \delta\Omega[z]. Figure 3.6 shows the three conditions that make up Kirchoffs three laws for creating, Copyright 2023 TipsFolder.com | Powered by Astra WordPress Theme. Definition. For ill-posed problems of the form \ref{eq1} the question arises: What is meant by an approximate solution? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Is it possible to rotate a window 90 degrees if it has the same length and width? had been ill for some years. What can a lawyer do if the client wants him to be acquitted of everything despite serious evidence? How can we prove that the supernatural or paranormal doesn't exist? Magnitude is anything that can be put equal or unequal to another thing. An operator $R(u,\alpha)$ from $U$ to $Z$, depending on a parameter $\alpha$, is said to be a regularizing operator (or regularization operator) for the equation $Az=u$ (in a neighbourhood of $u=u_T$) if it has the following properties: 1) there exists a $\delta_1 > 0$ such that $R(u,\alpha)$ is defined for every $\alpha$ and any $u_\delta \in U$ for which $\rho_U(u_\delta,u_T) < \delta \leq \delta_1$; and 2) there exists a function $\alpha = \alpha(\delta)$ of $\delta$ such that for any $\epsilon > 0$ there is a $\delta(\epsilon) \leq \delta_1$ such that if $u_\delta \in U$ and $\rho_U(u_\delta,u_T) \leq \delta(\epsilon)$, then $\rho_Z(z_\delta,z_T) < \epsilon$, where $z_\delta = R(u_\delta,\alpha(\delta))$. Now, how the term/s is/are used in maths is a . It only takes a minute to sign up. The so-called smoothing functional $M^\alpha[z,u_\delta]$ can be introduced formally, without connecting it with a conditional extremum problem for the functional $\Omega[z]$, and for an element $z_\alpha$ minimizing it sought on the set $F_{1,\delta}$. It can be regarded as the result of applying a certain operator $R_1(u_\delta,d)$ to the right-hand side of the equation $Az = u_\delta$, that is, $z_\delta=R_1(u_\delta,d)$. Select one of the following options. and the parameter $\alpha$ can be determined, for example, from the relation (see [TiAr]) Answers to these basic questions were given by A.N. grammar. Is there a proper earth ground point in this switch box? Some simple and well-defined problems are known as well-structured problems, and they have a set number of possible solutions; solutions are either 100% correct or completely incorrect. [V.I. Poorly defined; blurry, out of focus; lacking a clear boundary. A typical mathematical (2 2 = 4) question is an example of a well-structured problem. Here are seven steps to a successful problem-solving process. As an example, take as $X$ the set of all convex polygons, and take as $E$ "having the same number of edges". Dem Let $A$ be an inductive set, that exists by the axiom of infinity (AI). the principal square root). The element $z_\alpha$ minimizing $M^\alpha[z,u_\delta]$ can be regarded as the result of applying to the right-hand side of the equation $Az = u_\delta$ a certain operator $R_2(u_\delta,\alpha)$ depending on $\alpha$, that is, $z_\alpha = R_2(u_\delta,\alpha)$ in which $\alpha$ is determined by the discrepancy relation $\rho_U(Az_\alpha,u_\delta) = \delta$. Under these conditions, for every positive number $\delta < \rho_U(Az_0,u_\delta)$, where $z_0 \in \set{ z : \Omega[z] = \inf_{y\in F}\Omega[y] }$, there is an $\alpha(\delta)$ such that $\rho_U(Az_\alpha^\delta,u_\delta) = \delta$ (see [TiAr]). &\implies 3x \equiv 3y \pmod{24}\\ Groetsch, "The theory of Tikhonov regularization for Fredholm equations of the first kind", Pitman (1984), F. John, "Continuous dependence on data for solutions of partial differential equations with a prescribed bound", M. Kac, "Can one hear the shape of a drum? Let $\tilde{u}$ be this approximate value. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Next, suppose that not only the right-hand side of \ref{eq1} but also the operator $A$ is given approximately, so that instead of the exact initial data $(A,u_T)$ one has $(A_h,u_\delta)$, where Similarly approximate solutions of ill-posed problems in optimal control can be constructed. Phillips, "A technique for the numerical solution of certain integral equations of the first kind". Methods for finding the regularization parameter depend on the additional information available on the problem. Here are the possible solutions for "Ill-defined" clue. Other problems that lead to ill-posed problems in the sense described above are the Dirichlet problem for the wave equation, the non-characteristic Cauchy problem for the heat equation, the initial boundary value problem for the backwardheat equation, inverse scattering problems ([CoKr]), identification of parameters (coefficients) in partial differential equations from over-specified data ([Ba2], [EnGr]), and computerized tomography ([Na2]). &\implies h(\bar x) = h(\bar y) \text{ (In $\mathbb Z_{12}$).} An expression is said to be ambiguous (or poorly defined) if its definition does not assign it a unique interpretation or value. vegan) just to try it, does this inconvenience the caterers and staff? This is a regularizing minimizing sequence for the functional $f_\delta[z]$ (see [TiAr]), consequently, it converges as $n \rightarrow \infty$ to an element $z_0$. What is an example of an ill defined problem? Overview ill-defined problem Quick Reference In the study of problem solving, any problem in which either the starting position, the allowable operations, or the goal state is not clearly specified, or a unique solution cannot be shown to exist. poorly stated or described; "he confuses the reader with ill-defined terms and concepts". Beck, B. Blackwell, C.R. Evidently, $z_T = A^{-1}u_T$, where $A^{-1}$ is the operator inverse to $A$. Prior research involving cognitive processing relied heavily on instructional subjects from the areas of math, science and technology. Vldefinierad. The Radiology Assistant : Osteolytic - ill defined The axiom of subsets corresponding to the property $P(x)$: $\qquad\qquad\qquad\qquad\qquad\qquad\quad$''$x$ belongs to every inductive set''. Proving a function is well defined - Mathematics Stack Exchange Ambiguous -- from Wolfram MathWorld Stone, "Improperly posed boundary value problems", Pitman (1975), A.M. Cormak, "Representation of a function by its line integrals with some radiological applications". What is the appropriate action to take when approaching a railroad. To manage your alert preferences, click on the button below. A regularizing operator can be constructed by spectral methods (see [TiAr], [GoLeYa]), by means of the classical integral transforms in the case of equations of convolution type (see [Ar], [TiAr]), by the method of quasi-mappings (see [LaLi]), or by the iteration method (see [Kr]). Your current browser may not support copying via this button. It might differ depending on the context, but I suppose it's in a context that you say something about the set, function or whatever and say that it's well defined. To test the relation between episodic memory and problem solving, we examined the ability of individuals with single domain amnestic mild cognitive impairment (aMCI), a . The use of ill-defined problems for developing problem-solving and empirical skills in CS1, All Holdings within the ACM Digital Library. Hilbert's problems - Wikipedia In this context, both the right-hand side $u$ and the operator $A$ should be among the data. Problems of solving an equation \ref{eq1} are often called pattern recognition problems. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? As a result, what is an undefined problem? The statement '' well defined'' is used in many different contexts and, generally, it means that something is defined in a way that correspond to some given ''definition'' in the specific context. As these successes may be applicable to ill-defined domains, is important to investigate how to apply tutoring paradigms for tasks that are ill-defined. Designing Pascal Solutions: A Case Study Approach. Discuss contingencies, monitoring, and evaluation with each other. As a result, students developed empirical and critical-thinking skills, while also experiencing the use of programming as a tool for investigative inquiry. This is ill-defined when $H$ is not a normal subgroup since the result may depend on the choice of $g$ and $g'$. Resources for learning mathematics for intelligent people? See also Ambiguous, Ill-Posed , Well-Defined Explore with Wolfram|Alpha More things to try: partial differential equations 4x+3=19 conjugate: 1+3i+4j+3k, 1+-1i-j+3k Cite this as: Weisstein, Eric W. "Ill-Defined." Proving $\bar z_1+\bar z_2=\overline{z_1+z_2}$ and other, Inducing a well-defined function on a set. The following problems are unstable in the metric of $Z$, and therefore ill-posed: the solution of integral equations of the first kind; differentiation of functions known only approximately; numerical summation of Fourier series when their coefficients are known approximately in the metric of $\ell_2$; the Cauchy problem for the Laplace equation; the problem of analytic continuation of functions; and the inverse problem in gravimetry. Dari segi perumusan, cara menjawab dan kemungkinan jawabannya, masalah dapat dibedakan menjadi masalah yang dibatasi dengan baik (well-defined), dan masalah yang dibatasi tidak dengan baik. Should Computer Scientists Experiment More? Is this the true reason why $w$ is ill-defined? I have a Psychology Ph.D. focusing on Mathematical Psychology/Neuroscience and a Masters in Statistics. w = { 0, 1, 2, } = { 0, 0 +, ( 0 +) +, } (for clarity is changed to w) I agree that w is ill-defined because the " " does not specify how many steps we will go. The best answers are voted up and rise to the top, Not the answer you're looking for? because Symptoms, Signs, and Ill-Defined Conditions (780-799) This section contains symptoms, signs, abnormal laboratory or other investigative procedures results, and ill-defined conditions for which no diagnosis is recorded elsewhere. What is an example of an ill defined problem? - TipsFolder.com As a normal solution of a corresponding degenerate system one can take a solution $z$ of minimal norm $\norm{z}$. One distinguishes two types of such problems. This holds under the conditions that the solution of \ref{eq1} is unique and that $M$ is compact (see [Ti3]). Soc. Dealing with Poorly Defined Problems in an Agile World Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Test your knowledge - and maybe learn something along the way. The best answers are voted up and rise to the top, Not the answer you're looking for? For any positive number $\epsilon$ and functions $\beta_1(\delta)$ and $\beta_2(\delta)$ from $T_{\delta_1}$ such that $\beta_2(0) = 0$ and $\delta^2 / \beta_1(\delta) \leq \beta_2(\delta)$, there exists a $\delta_0 = \delta_0(\epsilon,\beta_1,\beta_2)$ such that for $u_\delta \in U$ and $\delta \leq \delta_0$ it follows from $\rho_U(u_\delta,u_T) \leq \delta$ that $\rho_Z(z^\delta,z_T) \leq \epsilon$, where $z^\alpha = R_2(u_\delta,\alpha)$ for all $\alpha$ for which $\delta^2 / \beta_1(\delta) \leq \alpha \leq \beta_2(\delta)$.

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