Sentence examples for accumulation points from inspiring English sources

"Closed" is a precise term meaning that it contains all its limit points, or accumulation points (the points such that no matter how close one comes to any of them, other points in the figure, or set, will be within that distance).

have no accumulation points, we have (3.9).

Moreover, {x k } and {z k } have the same weak accumulation points.

Furthermore, α(x n ) converges to α∗, and α(x∗)= α∗ for all accumulation points x∗.

Since the sequence { x k } k = 0 ∞ is bounded, it has weak accumulation points.

(3.13) Consequently, we see that ({x_{k}}) and ({y_{k}}) have the same weak accumulation points.

Let be an accumulation point of.

Since ({x^{k}}) is bounded, it has an accumulation point.

The corresponding accumulation point for a risk seeker was 90%.

Since (x^) was taken as an arbitrary accumulation point of ({x^{k}}), it follows that x̄ is the unique accumulation point of this sequence.

Since x ∗ was taken as an arbitrary weak accumulation point of { x k } k = 0 ∞, it follows that x ¯ is the unique weak accumulation point of this sequence.