Chapter 12: Q. 3 (page 987)

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* an open disk in $ℝ^{2}$ .

Short Answer

Expert verified

$L e t \in > 0 . L e t (x_{0}, y_{0}) \in ℝ^{2} . A s u b s e t o f ℝ^{2} o f t h e f o r m \{(x, y) | {(x - x_{0})}^{2} + {(y - y_{0})}^{2} < \in\} i s s a i d t o b e a n o p e n d i s k i n ℝ^{2} .$

Step by step solution

Step 1. Given Information.

An open disk in $ℝ^{2}$ .

Step 2. Definition.

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* an open disk in $ℝ^{2}$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Definition.

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Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.* an open disk in ℝ2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Definition.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Pure Maths

Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.
* an open disk in $ℝ^{2}$ .