What is the union of all of the closed intervals contained in the open interval (0, 1)? justify your answer.

Answers

After then, there must be some closed interval A between 0 and 1 such that x is less than A. As a result, x must fall between 0 and 1, as was intended.

This is further explained below.

What is the union of all of the closed intervals contained in the open interval (0, 1)?

Generally, Let A represents the set of all of the closed intervals that are included in (0, 1). Our contention is that A = (0, 1). To demonstrate this, let’s begin by demonstrating that the left-hand side contains the right-hand side in its entirety.

Let x ∈ (0, 1). Our goal is to demonstrate that there is at least one A A such that x A. We may define A to be the closed interval [x, x] that contains the single point x. Alternatively, if you don’t wish to state that a point is an interval, we can take A to be something like [x/2, x] or [x/2, (x + 1)/2] as an alternative.

In conclusion, because x > A > A, we may deduce that x > A A A. Now we will perform the confinement in the other direction. Let’s say that x > AA A.

If this is the case, there must be some closed interval A between 0 and 1 such that x falls inside A. Therefore, x should be between 0 and 1, as required.

theremust be some closed interval A between 0 and 1 such that x isless thanA. As a result, x must fall between 0 and 1, as was intended.## What is the union of all of the closed intervals contained in the open interval (0, 1)?

demonstratingthat the left-hand sidecontainsthe right-hand side in its entirety.Alternatively, if you don’t wish to state that a point is an interval, we can take A to be something like [x/2, x] or [x/2, (x + 1)/2] as an alternative.deducethat x > A A A. Now we will perform the confinement in the other direction. Let’s say that x > AA A.Therefore, x should be between 0 and 1, as required.intervalshttps://brainly.com/question/13708942