Hi. Which is correct? Let's say each had an (one) eraser. Thank you in advance for your help.
Each had their own eraser (or erasers).
In careful or formal English, we should (in my opinion) say: Each had his or her own eraser. However, singular "their" would in practice be commonplace. The fact that you use "their" to mean "his or her" shouldn't affect the fact that "eraser", singular, is the correct choice, but because "their" confuses the mind as to how many people are meant, you might see the plural used.
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In careful or formal English, we should (in my opinion) say:
Each had his or her own eraser.
However, singular "their" would in practice be commonplace. The fact that you use "their" to mean "his or her" shouldn't affect the fact that "eraser", singular, is the correct choice, but because "their" confuses the mind as to how many people are meant, you might see the plural use