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What are breakthroughs?

What are breakthroughs? Here are some definitions.

Noun
  1. plural of breakthrough
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Examples
True historical breakthroughs, in which the defender is shocked into inaction or headlong flight, are almost impossible to achieve.
You are more likely to have major breakthroughs when your line of thought isn't being interrupted.
Those breakthroughs alone would mean a virtually universally connected world.
Even before the breakthroughs that made long-distance fiber optics practical, aerospace engineers were trying to use photonic systems.
One of Penrose's major breakthroughs was his introduction of twistor theory in an attempt to unite relativity and quantum theory.
The secret to the Pool Putter's success are two key breakthroughs discovered by Swedish engineer Leif Sundberg.

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