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Brilliant_brown [7]
3 years ago
10

Fill in the blanks to rewrite the following statement with variables: Given any positive real number, there is a positive real n

umber that is smaller. (a) Given any positive real number r, there is s such that __________ s is __________ . (b) For any __________ , __________ such that s < r.
Mathematics
1 answer:
sveticcg [70]3 years ago
3 0

Answer:

a) there is s such that <u>r>s</u> and s is <u>positive</u>

b) For any <u>r>0</u> , <u>there exists s>0</u> such that s<r

Step-by-step explanation:

a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.

b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.

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