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, especially when vs we show by induction how to

These two phrases are not directly comparable as they serve different purposes. ", especially when" is used to emphasize a particular condition or situation, while "we show by induction how to" is used to introduce a method of proof. They are not interchangeable in a sentence.

Last updated: March 15, 2024 • 432 views

, especially when

This phrase is correct and commonly used in English to emphasize a specific condition or circumstance.

Use ", especially when" to highlight a particular situation or condition that is relevant to the context.
  • Use especially when something stands out from all the others, and you want the meaning of “particularly,” as in these examples: She can't be sure she will win, ...
  • Given all the other points that tend to set the population against war in general, it will become increasingly difficult to sell wars to populations, especially when ...
  • Another advised them how to dream, especially when they hit a setback. Sage Advice from Famous Dads Bruce Feiler June 18, 2010. Historical Examples.
  • Even If and Especially When is the second full-length album by the Seattle band Screaming Trees released in 1987. It was their first album released on the SST ...

we show by induction how to

This phrase is correct and commonly used in mathematical or logical contexts to introduce a method of proof by induction.

Use "we show by induction how to" to indicate the process of proving a statement using mathematical induction.
  • May 7, 2015 ... of length linear in the size of the formula F. Proof. We show by induction how to derive polynomials Pj = 1 − ∏ j i=1(1 − Ci) in length linear in j,.
  • Jun 11, 2008 ... We show by induction how to construct f and prove that the rectangular aspect ratio of each f(u) is at most 1/ǫ. This implies that the (standard) ...

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