How can I explain using (x0+ ε, x0-ε)? Explain why it is true that, if x0 is in (a,b), then there must be real numbers in (a,b) that are both smaller than and larger than x0. Why is this not necessarily true for [a,b]?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Please help me with this problem. How can I explain using (x0+ ε, x0-ε)?

Explain why it is true that, if xis in (a,b), then there must be real numbers in (a,b) that are both smaller than and larger than x0. Why is this not necessarily true for [a,b]?

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