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Because there are too many possibilities for the open covering. For a compact set, any family of open sets that covers can be replaced by a finite subfamily of open sets that still covers. Hence the open sets can't be too small.

Without compactness, the open sets can be quite small. For example, the infinite family of intervals (1/(n+1), 1/(n-1)) covers the open bounded set (0,1). (Here n is any integer larger than 1.) No subfamily will cover (0,1), and since the sets have radius going to zero, the Lebesgue number would also have to be zero.

Q: Why does the Lebesgue number not exist in a open and bounded set?

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open circle menas it is not part of the solution set and closed circle means that it is part of the solution

Math number models are tools used to develop computational strategies. Number models are often shown using physical representations such as: Base10 blocks, Ten Frames, Open Number Lines or a Number Grid amongst others. Using these models teachers can demonstrate various strategies such as "doubles". The problem 12+13 can be thought of as a "double" of 10 then 3+2

There are many software programs that will allow a person to make a flowchart to determine if the number is positive or negative. The person could use Open Office, Microsoft Word, Microsoft PowerPoint, or Microsoft Excel.

First tap on the plug that isn't in the outlet, in order to plug it in. The big 88 will appear. Each little piece of the number appears and disappears if you tap on it. Change the number to 35 (the floor number). Once you do that, the elevator doors will open. remove the lines on the numbers until you make a digital 35 on the doors

It doesn't have any open syllables.

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More than 1,100 open clusters have been discovered within the Milky Way Galaxy and many more are thought to exist.

Energy can enter or exist an open system

Energy can enter or exist an open system

To answer your question first here is the definition of polygon "a closed plane figure bounded by straight sides " So it makes no sense to count the sides in an open polygon since it is really not a polygon.

yes

OI is Open Interest. This refers to how many open contracts exist.

If the file doesn't exist, a warning to that effect will appear on the screen. The non-existent file will, naturally, fail to open.

No, because the games Open Seaon 2 and 3 don't exist.

No, it doesn't exist.

Open

A closed dot includes the number, an open dot excludes the number. Greater than excludes the number, so it would have an open dot.

You can't, it doesn't exist.