How many identities?

Algebra Level 3

Suppose SS is a set with a binary operation. Consider the following sentence about the identity elements in SS:

SS has 1234567\underline{\phantom{1234567}} left identities, 1234567\underline{\phantom{1234567}} right identities, and 1234567\underline{\phantom{1234567}} identity elements.

Which choice of words for the blanks gives a sentence that cannot be true?

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