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this lecturer is saying

Hello everyone. Welcome to the second lecture for CS230.

is it grammatical and idiomatic to add a "the" before an "ordinal number"?

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    In that sentence it is. You couldn't say welcome to second lecture - it would have to be welcome to lecture two of CS230.
    – user96060
    Jun 6 '19 at 1:14
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agree with @Minty, this case needs "the" before an "ordinal number", it would have to be welcome to lecture two of CS230.

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In the sentence

Welcome to the second lecture for CS230.

the definite article "the" is not only permitted but required. Some other uses also use the definite article, such as:

  • The Fifth Legion was stationed in what is now Germany.
  • The Fourth Horseman of the Apocalypse is Death.
  • The second book of the Torah is Exodus.
  • The Twentieth volume of O'Brian's series is Blue at the Mizzen.
  • The Fourth of July is a holiday in the united States, while the Fifth of November is celebrated in the United Kingdom.
  • The third chapter of the novel is the most exciting one.
  • I enjoyed the start, but when i reached the fifth chapter, I lost interest.
  • In "Sir Patrick Spens" I clean forgot the twenty-seventh verse, so I sang the forty-second twice as loud and in reverse, and no one noticed.
  • Hownblower's ship The Sutherland was a third-rate.

However some other uses of ordinals do not take articles.

  • Jones has won second place in today's race.
  • Second place goes to Jones.
  • It is good practice to design a database in fifth normal form.
  • Ballet dancers often speak of second and third position.
  • I shifted into third gear.
  • This restaurant is first-rate.

I can't clearly identify a general rule indicating when n article (definite or indefinite) is required, or customary in such uses.

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