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for each X_i vs for each x_i where

Both phrases are correct, but they are used in slightly different contexts. "For each x_i" is commonly used to introduce a general statement about each element x_i in a set, while "for each x_i where" is used when specifying a condition or constraint that x_i must satisfy.

Last updated: March 17, 2024 • 719 views

for each X_i

This phrase is correct and commonly used in English to introduce a general statement about each element x_i in a set.

This phrase is used to indicate that a statement applies to each individual element x_i in a set without specifying any conditions or constraints.

Examples:

  • For each x_i in the list, calculate the corresponding value.
  • For each x_i, there exists a unique y_i such that f(x_i) = y_i.
  • First, for each x_i, will have one node called "x_i" and one node called "not(x_i)". Let's call the three colors "red", "T" and "F", and add three special nodes in a ...
  • First, for each x_i, will have one node called "x_i" and one node called "not(x_i)". Let's call the three colors "red", "T" and "F", and add three special nodes in a ...
  • This means that it uses the following approximation for each x_i: df f(x_i+h) − f(x_i ) ---- = -------------------- dx_i h. for an appropriate small change in x_i, h, holding ...
  • Then by linearity of expectation, E(S_n) = np. What above Var(S_n)? For each X_i, we have Var(X_i) = E(X_i^2) - E(X_i)^2 = p - p^2 = p(1-p), Then we notice that ...

Alternatives:

  • for every x_i
  • for all x_i
  • for any x_i
  • for each element x_i

for each x_i where

This phrase is correct and is used when specifying a condition or constraint that x_i must satisfy.

This phrase is used to introduce a statement that applies to each element x_i in a set, subject to a specific condition or constraint.

Examples:

  • For each x_i where x_i > 0, calculate the corresponding value.
  • For each x_i where x_i is a prime number, there exists a unique y_i such that f(x_i) = y_i.

Alternatives:

  • for every x_i where
  • for all x_i where
  • for any x_i where
  • for each element x_i where

Related Comparisons

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