If "dots" are not really something we can use to define something, then what notation should we use instead? &\implies 3x \equiv 3y \pmod{24}\\ Tikhonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. 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 $M$. poorly stated or described; "he confuses the reader with ill-defined terms and concepts". M^\alpha[z,f_\delta] = f_\delta[z] + \alpha \Omega[z] The parameter $\alpha$ is determined from the condition $\rho_U(Az_\alpha,u_\delta) = \delta$. b: not normal or sound. Is there a detailed definition of the concept of a 'variable', and why do we use them as such? They include significant social, political, economic, and scientific issues (Simon, 1973). (for clarity $\omega$ is changed to $w$). For instance, it is a mental process in psychology and a computerized process in computer science. This is a regularizing minimizing sequence for the functional $f_\delta[z]$ (see [TiAr]), consequently, it converges as $n \rightarrow \infty$ to an element $z_0$. It is assumed that the equation $Az = u_T$ has a unique solution $z_T$. ill-defined. Is there a single-word adjective for "having exceptionally strong moral principles"? Is it suspicious or odd to stand by the gate of a GA airport watching the planes? I see "dots" in Analysis so often that I feel it could be made formal. You may also encounter well-definedness in such context: There are situations when we are more interested in object's properties then actual form. Clearly, it should be so defined that it is stable under small changes of the original information. Az = \tilde{u}, another set? This page was last edited on 25 April 2012, at 00:23. Axiom of infinity seems to ensure such construction is possible. Soc. $$(d\omega)(X_0,\dots,X_{k})=\sum_i(-1)^iX_i(\omega(X_0,\dots \hat X_i\dots X_{k}))+\sum_{i