Question

Является ли симметричным данное множество : [-3;3] (- бесконечности ; + бесконнечности ).. Объясните как это делать, НУЖНО ТОЛЬКО ОБЪЯСНЕНИЕ , ПОЖАЛУЙСТА. объяснитеее

Answer 1

Данные множества симметричны относительно нуля.

Множество симметрично относительно нуля, если для каждого х из этого множества (-х) тоже принадлежит множеству. 

Answer 2

Symmetry of the Set [-3;3] U (-∞; ∞)

The set [-3;3] U (-∞; ∞) consists of two parts: the closed interval [-3, 3] and the union with the entire real number line excluding the interval [-3, 3]. To determine if this set is symmetric, we need to check if it is unchanged when reflected across the y-axis.

To do this, we can examine the elements of the set and their corresponding reflections. The set [-3;3] U (-∞; ∞) contains all real numbers greater than or equal to -3 and less than or equal to 3, as well as all real numbers less than -3 or greater than 3.

Let's consider a few examples to determine if the set is symmetric:

1. Take the number 2. This number is in the set [-3;3] U (-∞; ∞). When reflected across the y-axis, it remains in the set [-3;3] U (-∞; ∞). Therefore, the set is symmetric with respect to the number 2.

2. Now consider the number -4. This number is not in the set [-3;3] U (-∞; ∞) since it is less than -3. When reflected across the y-axis, it remains outside the set [-3;3] U (-∞; ∞). Therefore, the set is not symmetric with respect to the number -4.

Based on these examples, we can conclude that the set [-3;3] U (-∞; ∞) is not symmetric. It contains elements that do not remain in the set when reflected across the y-axis.

I hope this explanation helps! Let me know if you have any further questions.