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Actually in Korea it is called lunar new years (seollal 설날). It's definitely the most important holiday of the year.
Everyone gets 4 days off this year, but my company is generous so I get one more day.

We will eat rice cake soup because we all turn one year older. So technically a baby born on december 31st 2019 will turn 2 on this Saturday, eventhough the been out for only a month.

Yes, lunar new year makes sense because it is based on the lunar calender that doesn't really belong to any specific country. Though I am surprised to learn its the most important holiday of the year, seems like Confucianism has a much deeper influence than I thought.

The Chinese have the same thing as well, the baby is considered one year old when born