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where x denote vs number of operations required to

These two phrases are not directly comparable as they serve different purposes. 'Where x denote' is used to introduce a variable or symbol in a mathematical context, while 'number of operations required to' is used to describe the quantity of operations needed to achieve a certain outcome. They are not interchangeable.

Last updated: March 17, 2024 • 557 views

where x denote

This phrase is correct when introducing a variable or symbol in a mathematical context.

This phrase is commonly used in mathematical writing to specify the meaning of a variable or symbol.

Examples:

  • Consider the equation y = 2x, where x denotes the input variable.
  • Let Sd = {x : x = 1} denote the unit sphere in Rd+1, where x denote the usual Euclidean norm. In the literature, the best Lp approximation by polynomials.
  • Let Sd = {x : x = 1} denote the unit sphere in Rd+1, where x denote the usual Euclidean norm. For a nonzero vector v ∈ Rd+1, let σv denote the reflection.
  • May 3, 2010 ... k ≤ n, where [x] denote the integer part of x. This extends and rafines previous results of U. Haagerup, P. de la Harpe [8] on the classical.
  • R—>0> Ti{R)~^2ifKJl where X? denote the eigenvalues of A with respect to p(x) ordered by magnitude. 3. Outline of proofs. Denote the eigenvalues (ordered by ...

number of operations required to

This phrase is correct when describing the quantity of operations needed to achieve a certain outcome.

This phrase is used to specify the total count of operations that are necessary to accomplish a task or reach a goal.

Examples:

  • The number of operations required to solve the problem is quite high.
  • Nov 7, 2014 ... The aim of this study was to determine the average number of operations required to complete breast reconstruction and to assess patient and ...
  • Find the minimum number of operations required to compute a number using a specified range of numbers. No problem. We won't show you ...
  • ... by counting the minimum number of operations required to transform one string into the other. Edit distances find applications in natural language processing, ...
  • The main difference of their approach and ours is that they are interested in the minimum number of operations required to produce one string from another, ...

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