Sentence examples for bounded thereby the sequence from inspiring English sources

Notice that F ( x ) is continuous on K, P K is continuous on R n and { x k } ⊆ K is bounded, the sequence { x ¯ k } is bounded, thereby the sequence { d k } is bounded.

Since is bounded, the sequence is bounded and nondecreasing.

If x0 ∈ E and the sequence is bounded, then the sequence is also bounded.

Since and are bounded, we have the sequence and hence the sequence is bounded.

Equivalently, a bounded operator T is compact if, for any bounded sequence {xk}, the sequence {Txk} has a convergent subsequence.

An example of an SNP is the substitution of a C for a G in the nucleotide sequence AACGAT, thereby producing the sequence AACCAT.

All of these time and space bounds are amortized over the sequence of operations.

Since the sequence is bounded, so and are bounded.

"O.K.," said Rae, turning her back and repeating the sequence, thereby delighting her dad.

Therefore, the sequence is bounded.

Thus, the sequence is bounded.