ill defined mathematics

Obviously, in many situation, the context is such that it is not necessary to specify all these aspect of the definition, and it is sufficient to say that the thing we are defining is '' well defined'' in such a context. Ill-Defined The term "ill-defined" is also used informally to mean ambiguous . Ill-defined. Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/ill-defined. You might explain that the reason this comes up is that often classes (i.e. Here are the possible solutions for "Ill-defined" clue. 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 $\rho_U(Az_\alpha,u_\delta) = \delta$. A partial differential equation whose solution does not depend continuously on its parameters (including but not limited to boundary conditions) is said to be ill-posed. Compare well-defined problem. Under these conditions the procedure for obtaining an approximate solution is the same, only instead of $M^\alpha[z,u_\delta]$ one has to consider the functional A natural number is a set that is an element of all inductive sets. Whenever a mathematical object is constructed there is need for convincing arguments that the construction isn't ambigouos. d 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 $z_\delta = R(u_\delta,\alpha(\delta))$. For convenience, I copy parts of the question here: For a set $A$, we define $A^+:=A\cup\{A\}$. Suppose that $Z$ is a normed space. For example we know that $\dfrac 13 = \dfrac 26.$. 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/ . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Computer 31(5), 32-40. You could not be signed in, please check and try again. A variant of this method in Hilbert scales has been developed in [Na] with parameter choice rules given in [Ne]. \label{eq1} Etymology: ill + defined How to pronounce ill-defined? \begin{equation} Arsenin, "On a method for obtaining approximate solutions to convolution integral equations of the first kind", A.B. \rho_U^2(A_hz,u_\delta) = \bigl( \delta + h \Omega[z_\alpha]^{1/2} \bigr)^2. Then $R_2(u,\alpha)$ is a regularizing operator for \ref{eq1}. Spangdahlem Air Base, Germany. Instead, saying that $f$ is well-defined just states the (hopefully provable) fact that the conditions described above hold for $g,h$, and so we really have given a definition of $f$ this way. Well-Defined vs. Ill-Defined Problems - alitoiu.com Select one of the following options. Let $\set{\delta_n}$ and $\set{\alpha_n}$ be null-sequences such that $\delta_n/\alpha_n \leq q < 1$ for every $n$, and let $\set{z_{\alpha_n,\delta_n}} $ be a sequence of elements minimizing $M^{\alpha_n}[z,f_{\delta_n}]$. Enter a Crossword Clue Sort by Length Dem Let $A$ be an inductive set, that exists by the axiom of infinity (AI). The main goal of the present study was to explore the role of sleep in the process of ill-defined problem solving. (eds.) Experiences using this particular assignment will be discussed, as well as general approaches to identifying ill-defined problems and integrating them into a CS1 course. adjective badly or inadequately defined; vague: He confuses the reader with ill-defined terms and concepts. PDF Chapter 12 - Problem Solving Definitions - Simon Fraser University Understand everyones needs. The next question is why the input is described as a poorly structured problem. Unstructured problems are the challenges that an organization faces when confronted with an unusual situation, and their solutions are unique at times. ill health. 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. National Association for Girls and Women in Sports (2001). From: The axiom of subsets corresponding to the property $P(x)$: $\qquad\qquad\qquad\qquad\qquad\qquad\quad$''$x$ belongs to every inductive set''. Ill-defined problem - Oxford Reference Identify the issues. How to handle a hobby that makes income in US. (1994). Third, organize your method. Understand everyones needs. Goncharskii, A.S. Leonov, A.G. Yagoda, "On the residual principle for solving nonlinear ill-posed problems", V.K. \rho_Z(z,z_T) \leq \epsilon(\delta), StClair, "Inverse heat conduction: ill posed problems", Wiley (1985), W.M. Sophia fell ill/ was taken ill (= became ill) while on holiday. Mode Definition in Statistics A mode is defined as the value that has a higher frequency in a given set of values. Is there a difference between non-existence and undefined? Morozov, "Methods for solving incorrectly posed problems", Springer (1984) (Translated from Russian), F. Natterer, "Error bounds for Tikhonov regularization in Hilbert scales", F. Natterer, "The mathematics of computerized tomography", Wiley (1986), A. Neubauer, "An a-posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates", L.E. 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 $M$. Ill-defined definition and meaning | Collins English Dictionary So-called badly-conditioned systems of linear algebraic equations can be regarded as systems obtained from degenerate ones when the operator $A$ is replaced by its approximation $A_h$. The theorem of concern in this post is the Unique Prime. Copyright 2023 ACM, Inc. Journal of Computing Sciences in Colleges. In mathematics, an expression is well-defined if it is unambiguous and its objects are independent of their representation. It is widely used in constructions with equivalence classes and partitions.For example when H is a normal subgroup of the group G, we define multiplication on G/H by aH.bH=abH and say that it is well-defined to mean that if xH=aH and yH=bH then abH=xyH. Mode | Mode in Statistics (Definition, How to Find Mode, Examples) - BYJUS For example, the problem of finding a function $z(x)$ with piecewise-continuous second-order derivative on $[a,b]$ that minimizes the functional Ill-defined Definition & Meaning - Merriam-Webster Lavrent'ev, V.G. - Henry Swanson Feb 1, 2016 at 9:08 Can these dots be implemented in the formal language of the theory of ZF? Are there tables of wastage rates for different fruit and veg? For such problems it is irrelevant on what elements the required minimum is attained. As a pointer, having the axiom of infinity being its own axiom in ZF would be rather silly if this construction was well-defined. The function $\phi(\alpha)$ is monotone and semi-continuous for every $\alpha > 0$. Furthermore, Atanassov and Gargov introduced the notion of Interval-valued intuitionistic fuzzy sets (IVIFSs) extending the concept IFS, in which, the . Make it clear what the issue is. It is not well-defined because $f(1/2) = 2/2 =1$ and $f(2/4) = 3/4$. Nonlinear algorithms include the . As a result, what is an undefined problem? Such problems are called essentially ill-posed. Let $\Omega[z]$ be a stabilizing functional defined on a subset $F_1$ of $Z$. Ill-posed problem | Article about ill-posed problem by The Free Dictionary Axiom of infinity seems to ensure such construction is possible. 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. 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). $$ Is it suspicious or odd to stand by the gate of a GA airport watching the planes? If we use infinite or even uncountable many $+$ then $w\neq \omega_0=\omega$. Semi structured problems are defined as problems that are less routine in life. an ill-defined mission. Buy Primes are ILL defined in Mathematics // Math focus: Read Kindle Store Reviews - Amazon.com Amazon.com: Primes are ILL defined in Mathematics // Math focus eBook : Plutonium, Archimedes: Kindle Store Definition. A second question is: What algorithms are there for the construction of such solutions? ill weather. By poorly defined, I don't mean a poorly written story. vegan) just to try it, does this inconvenience the caterers and staff? A function that is not well-defined, is actually not even a function. relationships between generators, the function is ill-defined (the opposite of well-defined). The answer to both questions is no; the usage of dots is simply for notational purposes; that is, you cannot use dots to define the set of natural numbers, but rather to represent that set after you have proved it exists, and it is clear to the reader what are the elements omitted by the dots. See also Ill-Defined, Well-Defined Explore with Wolfram|Alpha More things to try: Beta (5, 4) feigenbaum alpha Cite this as: Primes are ILL defined in Mathematics // Math focus Kindle Edition The term problem solving has a slightly different meaning depending on the discipline. A problem statement is a short description of an issue or a condition that needs to be addressed. set theory - Why is the set $w={0,1,2,\ldots}$ ill-defined If the minimization problem for $f[z]$ has a unique solution $z_0$, then a regularizing minimizing sequence converges to $z_0$, and under these conditions it is sufficient to exhibit algorithms for the construction of regularizing minimizing sequences. 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. In most (but not all) cases, this applies to the definition of a function $f\colon A\to B$ in terms of two given functions $g\colon C\to A$ and $h\colon C\to B$: For $a\in A$ we want to define $f(a)$ by first picking an element $c\in C$ with $g(c)=a$ and then let $f(a)=h(c)$. ($F_1$ can be the whole of $Z$.) 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? $$ Well-defined expression - Wikipedia Disequilibration for Teaching the Scientific Method in Computer Science. Let $\Omega[z]$ be a continuous non-negative functional defined on a subset $F_1$ of $Z$ that is everywhere-dense in $Z$ and is such that: a) $z_1 \in F_1$; and b) for every $d > 0$ the set of elements $z$ in $F_1$ for which $\Omega[z] \leq d$, is compact in $F_1$. In the comment section of this question, Thomas Andrews say that the set $w=\{0,1,2,\cdots\}$ is ill-defined. 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 $\rho_U(u_\delta,u_T) \leq \delta$. No, leave fsolve () aside. Enter the length or pattern for better results. Let $\Omega[z]$ be a stabilizing functional defined on a set $F_1 \subset Z$, let $\inf_{z \in F_1}f[z] = f[z_0]$ and let $z_0 \in F_1$. David US English Zira US English What is the best example of a well-structured problem, in addition? 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]). How should the relativized Kleene pointclass $\Sigma^1_1(A)$ be defined? this function is not well defined. A quasi-solution of \ref{eq1} on $M$ is an element $\tilde{z}\in M$ that minimizes for a given $\tilde{u}$ the functional $\rho_U(Az,\tilde{u})$ on $M$ (see [Iv2]). . Send us feedback. A common addendum to a formula defining a function in mathematical texts is, "it remains to be shown that the function is well defined.". 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, $z_\delta=R_1(u_\delta,d)$. Therefore, as approximate solutions of such problems one can take the values of the functional $f[z]$ on any minimizing sequence $\set{z_n}$. Tip Two: Make a statement about your issue. I have encountered this term "well defined" in many places in maths like well-defined set, well-defined function, well-defined group, etc. This paper describes a specific ill-defined problem that was successfully used as an assignment in a recent CS1 course. set of natural number w is defined as. If you preorder a special airline meal (e.g. Let me give a simple example that I used last week in my lecture to pre-service teachers. Is the term "properly defined" equivalent to "well-defined"? Domains in which traditional approaches for building tutoring systems are not applicable or do not work well have been termed "ill-defined domains." This chapter provides an updated overview of the problems and solutions for building intelligent tutoring systems for these domains. 2023. What is the best example of a well structured problem? The European Mathematical Society, incorrectly-posed problems, improperly-posed problems, 2010 Mathematics Subject Classification: Primary: 47A52 Secondary: 47J0665F22 [MSN][ZBL] In practice the search for $z_\delta$ can be carried out in the following manner: under mild addition 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. For example, a set that is identified as "the set of even whole numbers between 1 and 11" is a well-defined set because it is possible to identify the exact members of the set: 2, 4, 6, 8 and 10. \int_a^b K(x,s) z(s) \rd s. If "dots" are not really something we can use to define something, then what notation should we use instead? Vinokurov, "On the regularization of discontinuous mappings", J. Baumeister, "Stable solution of inverse problems", Vieweg (1986), G. Backus, F. Gilbert, "The resolving power of gross earth data", J.V. ILL | English meaning - Cambridge Dictionary Do new devs get fired if they can't solve a certain bug? Mathematicians often do this, however : they define a set with $$ or a sequence by giving the first few terms and saying that "the pattern is obvious" : again, this is a matter of practice, not principle. If we want $w=\omega_0$ then we have to specify that there can only be finitely many $+$ above $0$. Methods for finding the regularization parameter depend on the additional information available on the problem. The regularization method is closely connected with the construction of splines (cf. Spline). In many cases the operator $A$ is such that its inverse $A^{-1}$ is not continuous, for example, when $A$ is a completely-continuous operator in a Hilbert space, in particular an integral operator of the form 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. The parameter $\alpha$ is determined from the condition $\rho_U(Az_\alpha,u_\delta) = \delta$. An expression is said to be ambiguous (or poorly defined) if its definition does not assign it a unique interpretation or value. The Tower of Hanoi, the Wason selection task, and water-jar issues are all typical examples. 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? It generalizes the concept of continuity . Otherwise, the expression is said to be not well defined, ill definedor ambiguous. PRINTED FROM OXFORD REFERENCE (www.oxfordreference.com). Mutually exclusive execution using std::atomic? Math. Ill-defined problem solving in amnestic mild cognitive - PubMed Is there a detailed definition of the concept of a 'variable', and why do we use them as such? https://encyclopediaofmath.org/index.php?title=Ill-posed_problems&oldid=25322, Numerical analysis and scientific computing, V.Ya. $$ The ACM Digital Library is published by the Association for Computing Machinery. Dec 2, 2016 at 18:41 1 Yes, exactly. What is the appropriate action to take when approaching a railroad. [ 1] En funktion dremot r vldefinierad nr den ger samma resultat d ingngsvrdets representativa vrde ndras utan att dess kvantitiva vrde gr det. 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. ill deeds. What is the best example of a well structured problem? M^\alpha[z,f_\delta] = f_\delta[z] + \alpha \Omega[z] The link was not copied. Boerner, A.K. $$ Also called an ill-structured problem. (c) Copyright Oxford University Press, 2023. The construction of regularizing operators. Since $u_T$ is obtained by measurement, it is known only approximately. Vldefinierad. 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. ILL defined primes is the reason Primes have NO PATTERN, have NO FORMULA, and also, since no pattern, cannot have any Theorems. It was last seen in British general knowledge crossword. Mathematics is the science of the connection of magnitudes. 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$. Teach ill-structured problem solving with discussion | iTeachU 1 Introduction Domains where classical approaches for building intelligent tutoring systems (ITS) are not applicable or do not work well have been termed "ill-defined domains" [1]. Huba, M.E., & Freed, J.E. 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. Most common location: femur, iliac bone, fibula, rib, tibia. Learn a new word every day. The result is tutoring services that exceed what was possible to offer with each individual approach for this domain. approximating $z_T$. Soc. rev2023.3.3.43278. $\qquad\qquad\qquad\qquad\qquad\qquad\quad\quad$, $\varnothing,\;\{\varnothing\},\;\&\;\{\varnothing,\{\varnothing\}\}$, $\qquad\qquad\qquad\qquad\qquad\qquad\quad$. p\in \omega\ s.t\ m+p=n$, Using Replacement to prove transitive closure is a set without recursion. given the function $f(x)=\sqrt{x}=y$ such that $y^2=x$. \end{align}. Allyn & Bacon, Needham Heights, MA. Tip Two: Make a statement about your issue. But how do we know that this does not depend on our choice of circle? Multi Criteria Decision Making via Intuitionistic Fuzzy Set By Talukdar Well Defined Vs Not Well Defined Sets - YouTube Make sure no trains are approaching from either direction, The three spectroscopy laws of Kirchhoff. Let $z$ be a characteristic quantity of the phenomenon (or object) to be studied. 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. Origin of ill-defined First recorded in 1865-70 Words nearby ill-defined ill-boding, ill-bred, ill-conceived, ill-conditioned, ill-considered, ill-defined, ill-disguised, ill-disposed, Ille, Ille-et-Vilaine, illegal Reed, D., Miller, C., & Braught, G. (2000). Follow Up: struct sockaddr storage initialization by network format-string. &\implies h(\bar x) = h(\bar y) \text{ (In $\mathbb Z_{12}$).} set of natural number $w$ is defined as Jordan, "Inverse methods in electromagnetics", J.R. Cann on, "The one-dimensional heat equation", Addison-Wesley (1984), A. Carasso, A.P. Topology is a relatively new branch of mathematics; most of the research in topology has been done since 1900. The term "critical thinking" (CT) is frequently found in educational policy documents in sections outlining curriculum goals. $h:\mathbb Z_8 \to \mathbb Z_{12}$ defined by $h(\bar x) = \overline{3x}$. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. \label{eq2} In the second type of problems one has to find elements $z$ on which the minimum of $f[z]$ is attained. 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 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. Secondly notice that I used "the" in the definition. In fact, what physical interpretation can a solution have if an arbitrary small change in the data can lead to large changes in the solution? Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. $$ : For every $\epsilon > 0$ there is a $\delta(\epsilon) > 0$ such that for any $u_1, u_2 \in U$ it follows from $\rho_U(u_1,u_2) \leq \delta(\epsilon)$ that $\rho_Z(z_1,z_2) < \epsilon$, where $z_1 = R(u_1)$ and $z_2 = R(u_2)$. Tikhonov, "On the stability of the functional optimization problem", A.N. Beck, B. Blackwell, C.R. You may also encounter well-definedness in such context: There are situations when we are more interested in object's properties then actual form. Evidently, $z_T = A^{-1}u_T$, where $A^{-1}$ is the operator inverse to $A$. 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 $A$. Make it clear what the issue is. The question arises: When is this method applicable, that is, when does Can I tell police to wait and call a lawyer when served with a search warrant? This holds under the conditions that the solution of \ref{eq1} is unique and that $M$ is compact (see [Ti3]). 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. 2. a: causing suffering or distress. Its also known as a well-organized problem. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? PS: I know the usual definition of $\omega_0$ as the minimal infinite ordinal. Proceedings of the 34th Midwest Instruction and Computing Symposium, University of Northern Iowa, April, 2001. Is there a proper earth ground point in this switch box? Take an equivalence relation $E$ on a set $X$. Vldefinierad - Wikipedia ITS in ill-defined domains: Toward hybrid approaches - Academia.edu ", M.H. To save this word, you'll need to log in. \norm{\bar{z} - z_0}_Z = \inf_{z \in Z} \norm{z - z_0}_Z . The exterior derivative on $M$ is a $\mathbb{R}$ linear map $d:\Omega^*(M)\to\Omega^{*+1}(M)$ such that. In contrast to well-structured issues, ill-structured ones lack any initial clear or spelled out goals, operations, end states, or constraints. The selection method. This is a regularizing minimizing sequence for the functional $f_\delta[z]$ (see [TiAr]), consequently, it converges as $n \rightarrow \infty$ to an element $z_0$. Evaluate the options and list the possible solutions (options). If I say a set S is well defined, then i am saying that the definition of the S defines something? And it doesn't ensure the construction. 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. Why is the set $w={0,1,2,\ldots}$ ill-defined? Deconvolution -- from Wolfram MathWorld Ill defined Crossword Clue The Crossword Solver found 30 answers to "Ill defined", 4 letters crossword clue. It appears to me that if we limit the number of $+$ to be finite, then $w=\omega_0$. More examples Shishalskii, "Ill-posed problems of mathematical physics and analysis", Amer. Is it possible to rotate a window 90 degrees if it has the same length and width? What Is a Well-Defined Set in Mathematics? - Reference.com The school setting central to this case study was a suburban public middle school that had sustained an integrated STEM program for a period of over 5 years. There exists another class of problems: those, which are ill defined. grammar. So one should suspect that there is unique such operator $d.$ I.e if $d_1$ and $d_2$ have above properties then $d_1=d_2.$ It is also true. McGraw-Hill Companies, Inc., Boston, MA. il . Ill defined Crossword Clue | Wordplays.com 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). If $M$ is compact, then a quasi-solution exists for any $\tilde{u} \in U$, and if in addition $\tilde{u} \in AM$, then a quasi-solution $\tilde{z}$ coincides with the classical (exact) solution of \ref{eq1}. It is critical to understand the vision in order to decide what needs to be done when solving the problem. Document the agreement(s). ill-defined - English definition, grammar, pronunciation, synonyms and A Computer Science Tapestry (2nd ed.). An ill-defined problem is one in which the initial state, goal state, and/or methods are ill-defined.