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following that x vs follows that x

Both phrases are correct, but they are used in different contexts. 'Following that x' is used when referring to something that comes after a specific point in time or sequence, while 'follows that x' is used to introduce a consequence or result of a previous statement.

Last updated: March 19, 2024 • 637 views

following that x

This phrase is correct and commonly used in English.

This phrase is used to refer to something that comes after a specific point in time or sequence. It indicates a chronological or sequential order.

Examples:

  • Following that event, the company saw a significant increase in sales.
  • Following that meeting, we will proceed with the project.
  • Following that decision, the team implemented new strategies.
  • If xi = yi for all i ∈ {1, . . . , n}, then the inequality (1) holds with equality, hence we may assume in the following that xi ≠ yi for at least one i. If xi = yi for an i ∈ {1, ...
  • Show that the functions ρ and ρn are continuous and that the function un id of class C2. c. Write the Itô formula for un(Bt). We will admit in the following that x ∈ R ...
  • such a condition we mention the following, that /(x,X) may be uniformly approximated to by a sequence of functions. /i(x,X), each of which is integrable with ...
  • A solution of (2.1) and (2.4) is denoted by x(<f>o) and we assume in the following that x((f>o) exists and is unique on [?_i, oo). Remark!.].. It is known (see, e.g., ...

Alternatives:

  • After that x
  • Subsequent to that x
  • In the wake of that x
  • In the aftermath of that x
  • Following on from that x

follows that x

This phrase is correct and commonly used in English.

This phrase is used to introduce a consequence or result of a previous statement. It indicates a logical or causal relationship between two ideas.

Examples:

  • If we increase our marketing budget, follows that we will reach a wider audience.
  • If you study hard, follows that you will pass the exam.
  • If we invest in renewable energy, follows that we will reduce our carbon footprint.
  • Since x ∈ C - B, it follows that x ∈ C. Since x ∈ A and x ∈ C, it follows that x ∈ A n C. Since x ∈ A n C and x /∈ B, it follows that x ∈ (A n C) - B. We now show ...
  • appear to merge into one. Compare the clarity of the following examples. Because x2 −1 = 0, x = 1 or x = −1. ×. Because x2 −1 = 0, it follows that x = 1 or x = −1.
  • classes. If x1 ∈ [x], then x1 ∼ z and z ∼ y, so x1 ∼ y by the transitivity of ∼, and therefore x1 ∈ [y]. It follows that [x] ⊂ [y]. A similar argument applied to y1 ∈ [y].
  • follows that (x, y) /∈ R and (y, z) /∈ R, and hence xR/y and yR/z. By the contrapositive of the antitransitive property we have that xR/z. Hence. (x, z) /∈ R and (x, ...

Alternatives:

  • Consequently, x
  • Therefore, x
  • As a result, x
  • Hence, x
  • Thus, x

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