From this link
Spelling is very important in formal writing, but English spelling is very difficult.They’re aren’t too many rules, and most of them can be broken.
" The writer used the wrong "there/their/they're" -- it happens more than you would think. When I type quickly, I've been known to type the wrong here/hear or there/their -- not because I don't know the difference, but my fingers type what they "hear" my brain say and they sound the same. Still, in an edited work, someone should have noticed this.
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zillahThey’re aren’tNo one says they’re aren’t. The writer must have been a non-native or half asleep to make such a mistake.
Hi Yoong
It is hard for the publisher to admit that it is a mistake.