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, especially when vs we show by induction

These two phrases are not directly comparable as they serve different purposes. ", especially when" is used to introduce a specific circumstance or condition, while "we show by induction" is a phrase commonly used in mathematical proofs to demonstrate a result using the method of mathematical induction.

Last updated: March 15, 2024 • 634 views

, especially when

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

This phrase is used to provide additional information or context about a situation, emphasizing a particular condition or circumstance.
  • 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

This phrase is correct and commonly used in mathematical proofs to demonstrate a result using the method of mathematical induction.

This phrase is used in mathematical contexts to indicate that a proof is being carried out using the method of mathematical induction.
  • We show by induction that f3n is even, for all n. Clearly, f3 = 2 is even. Assume that f3k is even for a natural number k. Then f3(k+1) = f3k+3. = f3k+2 + f3k+1.
  • Now we show by induction that any bet of $48 or more CAN be placed. Let S be the set of all positive integers n such that there is a solution to n = 7x + 9y, where  ...
  • Now we show by induction on α that if α is a wff then the length of α is not. 2, 3,, or 6. Base Case: If α is a sentence symbol, the length of α is 1, which is not 2, 3,.
  • Oct 29, 2005 ... We show by induction that n(h) ≥ (1 + α)h −1, for some constant 0 < α ≤ 1. We can then conclude that for a tree with n nodes, h ≤ log. 1+α.

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