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What is the difference in meaning between

i equals 0 or 1.

and

i equals either 0 or 1.

?

I think both are grammatically correct, but I'm not sure if they have exactly the same meaning.

One example of "either… or…" structure from oxfordlearnersdictionaries.com:

Well, I think she's either Czech or Slovak.

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    I don't think there's really a difference. 'Either' is simply a word that one can use to introduce the comparison. As for your two examples, they both evaluate to i={0|1} logically. – Jakob Lovern Feb 22 '18 at 23:38
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Usually either does not change the meaning of the sentence and only serves to emphasize that:

  • there are exactly two choices possible
  • you cannot have both

In most sentences, this is already implied by or, and either is just emphatic. If the or by itself is inclusive, either will usually be exclusive (although not always):

This license allows you to drive a car or a truck. (you can drive both)

This license allows you to drive either a car or a truck. (it's possible you can drive both, but it's likely to mean you can drive only one of those eg. depending on the type of the license)

Also, in negative sentences either usually changes the meaning of the sentence, since negated or usually means "neither":

She couldn't read or write. (She couldn't read and she couldn't write.)

She could neither read nor write. (She couldn't read and she couldn't write.)

She couldn't either read or write. (She could read, but couldn't write OR She couldn't read, but she could write)

  • Can 'both' be used instead of 'either' in the last example? – apadana Feb 23 '18 at 0:05
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    @Arham "She couldn't both read and write" is more likely to mean "She couldn't read and she couldn't write" to me. – Maciej Stachowski Feb 23 '18 at 0:21

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