Is the following statement true or false? Let A C R. Then a E R is the supremum of A if and only if it is an upper bound for A and Về > 0]x € A:x> a- €.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Is the following statement true or false?
Let A CR. Then a ER is the supremum of A if and only if it is an upper bound
for A and Ve > 03x € A : x > a- €.
Transcribed Image Text:Is the following statement true or false? Let A CR. Then a ER is the supremum of A if and only if it is an upper bound for A and Ve > 03x € A : x > a- €.
Expert Solution
Step 1: Write the given information:

Let A subset of or equal to R then a element of R is the supremum of A if and only if it is an upper bound for A and for all epsilon greater than 0 there exists x element of A colon x greater than a minus epsilon.

To Find:

Is the above statement is true or false.


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