If someone owes you money and they say they will have it to you "by the first," doesn't that mean you will get it before the first of the month?
"By the first" is a fairly common idiom that has two general meanings, depending on the context. If the agreement is for a recurring payment, then payment will be rendered on the first day of each month or earlier. If the agreement is for a one time payment, then payment will be rendered on the first day of the next month or earlier. It's important to note that "by the first" includes the first day of the following month. In other words, if someone says "by the first," it usually means you will not get the money on the last day of the month. So, to directly answer your question:
doesn't that mean you will get it before the first of the month?
No. It does not mean that. You may receive the money on the first day of the month.
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This depends on the context. If it's rent, say, and it's monthly, then perhaps. Just make sure they don't mean I'll have it to you by the first of next year. It's also not uncommon to say things like the meeting is held the first Monday of each month or we have lunch every third Thursday.