Chapter 12: Q. 4 (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 ball in $ℝ^{3}$ .

Short Answer

Expert verified

$L e t \in > 0 . L e t (x_{0}, y_{0}, z_{0}) \in ℝ^{3} . A s u b s e t o f ℝ^{3} o f t h e f o r m \{(x, y) | {(x - x_{0})}^{2} + {(y - y_{0})}^{2} + {(z - z_{0})}^{2} < \in\} i s s a i d t o b e a n o p e n b a l l i n ℝ^{3} .$

Step by step solution

Step 1. Given Information.

An open ball in $ℝ^{3}$ .

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 ball in $ℝ^{3}$ .

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 ball inℝ3.

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

Logic and Functions

Applied Mathematics

Discrete Mathematics

Statistics

Geometry

Calculus

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 ball in $ℝ^{3}$ .