Sandwich theorems
Limits preserve non-strict inequalities: if for all and , then . Squeezing: if , and , then .
Proposition 1.6 (Sandwich Theorems)
Let , , be real sequences. Then
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If for all and , then .
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If , , and , then .
Important. The best conclusion in the case that for all and , is still .
Related
Stated in
- Proposition 1.6 (Sandwich Theorems)§1.1 Basics