Question

prove that any convergent sequence is a cauchy sequence​

Answer 1

Answer:

The proof is essentially the same as the corresponding result for convergent sequences. Any convergent sequence is a Cauchy sequence. If (an)→ α then given ε > 0 choose N so that if n > N we have |an- α| < ε. Then if m, n > N we have |am- an| = |(am- α) - (am- α)| ≤ |am- α| + |am- α| < 2ε

Answer 2

Answer:

Using a quantum computer to simulate time travel, researchers have demonstrated that, in the quantum realm, there is no 'butterfly effect. ' In the research, information--qubits, or quantum bits--'time travel' into the simulated past.