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• Precalculus
  The idea is to use this set-up to produce a correspondence: The idea is to use this set-up to produce a correspondence:
  100 KB (16,148 words) - 20:04, 18 January 2017
• Sequences and their limits
  A function defined on a ray in the set of integers, $\{p,p+1,...\}$, is called an ''infinite sequence'', or simply The last option is used when we treat the sequence as a ''set''.
  64 KB (10,809 words) - 02:11, 23 February 2019
• Classification of points with respect to a subset
  For the background see [[Introduction to point-set topology]]. Given a set $A$ in $X$,
  4 KB (703 words) - 01:55, 1 October 2013
• More about manifolds
  '''Dimension 1:''' When is a level set of $f \colon {\bf R} \rightarrow {\bf R}$ a $0$-manifold? Then we are looking at the intersection of the graph of $f$ and the plane $z=A$, around the point $(a,A)$. Since $f
  9 KB (1,542 words) - 19:58, 21 January 2014
• Applications of differential calculus
  In other words, we find the intersection of the tangent line with the $x$-axis: The equation, which is ''linear'', is easy to solve. The point of intersection is
  59 KB (10,063 words) - 04:59, 21 February 2019
• Vector and complex variables
  ...a line on the plane. Then the solution $(x,y)=(4,2)$ is the point of their intersection: ...equations represent two planes in ${\bf R}^3$. The solution is then their intersection:
  113 KB (18,750 words) - 02:33, 10 December 2018
• From continuity to point-set topology
  #redirect[[Introduction to point-set topology]] Our interest is mainly is algebraic topology. Consequently, point-set topology will be limited to that of the [[euclidean space]], "nice" subsets
  7 KB (1,207 words) - 13:01, 12 August 2015
• Discrete calculus article
  A '''simplicial complex''' <math>\mathcal{K}</math> is a set of [[Simplex|simplices]] that satisfies the following conditions: :2. The non-empty [[Set intersection|intersection]] of any two simplices <math>\sigma_1, \sigma_2 \in \mathcal{K}</math> is a
  27 KB (4,329 words) - 16:02, 1 September 2019
• Several variables
  ...s. The height at the end of the flight is $y_1=0$, so to find the time, we set $y=200-16t^2=0$ and solve for $t$: ...ordinates have make sense. Then, we can choose the domain of $F$ to be the intersection of the domains of $f$ and $g$.
  76 KB (13,017 words) - 20:26, 23 February 2019
• Intersection of a finite collection of open sets is open
  Prove that the [[intersection]] of a finite collection of [[open set]]s is open. ...e intersection of these neighborhoods. It will lie inside the intersection set.
  506 bytes (79 words) - 14:43, 23 February 2011
• Functions in higher dimensions
  *a ''circle'' on the plane is defined to be the set of all point a given distance away from its center; *a ''sphere'' in the space is defined to be the set of all point a given distance away from its center.
  113 KB (19,680 words) - 00:08, 23 February 2019
• Introductory algebraic topology: review exercises
  *[[Can a set to be both open and closed? ]] *[[Intersection of any collection of closed sets is closed ]]
  9 KB (1,553 words) - 20:10, 23 October 2012
• Parametric complexes
  ...persistence and can be removed when the threshold for acceptable noise is set. ...$ defined on a rectangle $R$. Then, given a threshold $r$, its lower level set $f^{-1}((-\infty,r))$ can be thought of as a binary image on $R$. Each blac
  45 KB (7,255 words) - 03:59, 29 November 2015
• A new look at continuity
  Now, an example of an especially “nice” set is ...ion $1$, this is simply a closed interval, yet functions defined on such a set won't fit into the last definition of continuity.
  17 KB (2,946 words) - 04:51, 25 November 2015
• Functions of several variables OLD
  [[Image:path-connected set.jpg|right]] '''Exercise.''' Apply the same proof to show that any [[convex set]] is path-connected (think of a box, a square, a 3d cylinder, etc).
  34 KB (5,636 words) - 23:52, 7 October 2017
• Vector functions
  ...R}^n {\rightarrow} {\bf R}$, then for each $c {\in} {\bf R}$ the ''[[level set]]'' relative to $c$ of $f$ is What would be a level set that is not a curve, but that isn't a maximum or a minimum?
  28 KB (4,769 words) - 19:42, 18 August 2011
• Implicit Function Theorem
  ...\bf R}^n \rightarrow {\bf R}$, then for each $c \in {\bf R}$ the ''[[level set]]'' relative to $c$ of $f$ is What would be a level set that is not a curve, but that isn't a maximum or a minimum?
  2 KB (400 words) - 20:29, 28 August 2011
• Calculus Illustrated -- Notation
  *$x\in X\quad$ “$x$ belongs to set $X$” or “$x$ is an element of $X$”; *$x\not\in X\quad$ “$x$ does not belongs to set $X$” or “$x$ is not an element of $X$”;
  2 KB (438 words) - 22:34, 22 June 2019
• Linear algebra: test 1
  #Prove that the set of all non-zero rational numbers, $\mathbf{Q}\backslash \{0\},$ is closed u #Prove that the intersection of two subspaces is always a subspace.
  4 KB (538 words) - 20:28, 9 September 2011
• Calculus III -- Fall 2017
  *[http://users.marshall.edu/~saveliev/Teaching/Fall17/math231/set01.pdf Set 1] *[http://users.marshall.edu/~saveliev/Teaching/Fall17/math231/set2.pdf Set 2]
  10 KB (1,596 words) - 13:34, 27 November 2017

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