Mathematics · Real Analysis

Which of the following statements is NOT true for sequences of real numbers?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1If and are two convergent sequences, then is always convergent.
2The range set of every real sequence is countable.
3If is any sequence and limn→• xn = 0, then limn→• (xn · yn) = 0.✓
4If and are two convergent sequences of real numbers such that xn ≤ yn for all n ∈ N, then lim xn ≤ lim yn.

Correct answer

If is any sequence and limn→• xn = 0, then limn→• (xn · yn) = 0.

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