The inference shows that the social position that the author had at the time of writing was in the 10 the century during the Heian period in Japan.
An inference simply means the conclusion that can be deduced based on the information that's given in a passage.
In this case, the social position that the author had at the time of writing was in the 10 the century during the Heian period in Japan.
It was about the observations of the author during her time as a court lady to Empress Consort Teishi.
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