Math Problem Statement

WHAT IS THE SET OF {x E R| -5 <x< 1

Solution

The set {xR5<x<1}\{x \in \mathbb{R} \mid -5 < x < 1\} represents all real numbers xx that are greater than 5-5 and less than 11.

In interval notation, this set is written as:

(5,1)(-5, 1)

This indicates that xx can take any value within the interval starting just above 5-5 and ending just below 11, but does not include 5-5 and 11 themselves.

Would you like to see any details or have any questions?

Here are 5 related questions you might consider:

  1. What would the interval be if xx were inclusive of 5-5 and 11?
  2. How would the set change if it were defined for integers instead of real numbers?
  3. What is the midpoint of the interval (5,1)(-5, 1)?
  4. How would the interval change if it were {xR1<x3}\{x \in \mathbb{R} \mid -1 < x \leq 3\}?
  5. How do you express the interval (,0)(-\infty, 0) in set-builder notation?

Tip: When writing intervals, remember that parentheses (( and )) indicate that the endpoints are not included in the set, while brackets [[ and )])] indicate that they are included.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Real Numbers
Inequalities
Interval Notation

Formulas

Interval Notation: (a, b) represents all real numbers between a and b where endpoints are excluded.

Theorems

Basic Set Theory: The concept of open intervals and real number sets.

Suitable Grade Level

Grades 9-12