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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 • 753 views

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

", especially when "

This phrase is used to provide additional information or context about a situation, emphasizing a particular condition or circumstance.
  • May 18, 2024 ... The Truth Hurts — Especially When Bill Maher Dishes It Out ... Back in 2013, I got a call from Bill Maher. He was being hit with a lawsuit by ...
  • Nov 11, 2011 ... Does 'especially' modify the word 'when' in the sentence below? Example: I like peanunt M&Ms, especially when I can find them on sale. Thanks,
  • Jan 26, 2017 ... How to Coach Like a Leader … Even (Especially) When You're a Skeptic · There's Good Reason to Be Skeptical … ·… Just Don't Be Cynical · A New Hope ...
  • I sing the body electric, especially when my power's out. This is my body, I have weather veins, They're especially sensitive to dust storms and hurricanes.
  • Apr 13, 2020 ... Setting boundaries is hard, especially when power dynamics are not in your favor. Here's how to do it right, whether you're working in an ...
  • Aug 17, 2024 ... 1085 likes, 9 comments - carterfaith on August 17, 2024: "i love playing shows especially when i get to open for my friends love you ...
  • Mar 11, 2019 ... Stuff Matters, Especially When You Risk “Everything” for It. Article metadata. Article length: 11 min read 2,151 words in 12 paragraphs ...
  • 19 hours ago ... GUIDs are amazing, especially when saving objects. ... I just started making a saving system for my game, and using GUIDs for all of my objects ...
  • Mar 30, 2011 ... Especially when the weather report predicts rain, you should have an umbrella in your car. In both of these examples you could change the ...
  • Jul 15, 2024 ... top surfaces are really uneven, especially when using 100% infill · Retraction: 3mm distance, 40mm/s speed, 0.1mm z-hop · Speed: 36mm/s on ...

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

"we show by 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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