correct English pronunciation of the word poset

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What is the correct English pronunciation of the word poset (Partially Ordered SET)?

paazit or pow-set?

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Neither...I would probably transliterate it as "poh-set". You definitely want to pronounce "set" as it's own syllable.

"Poh" rhymes with though, row, snow, toe, etc.

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PO-set.

"PO" rhymes with "snow".

At least in my neck of the woods...

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Poset rhymes with LOW-SET or ROW-SET. Similarly for woset (well-ordered set). Watch this YouTube video where Doctor Bob says POSET around 7:50.