

Although we performed...in this tutorial OR Although we HAVE performed...in this tutorial? - amichail

Are both forms acceptable?  It appears so according to Google:<p>http://www.google.ca/search?q=%22although+we+defined%22<p>http://www.google.ca/search?q=%22although+we+have+defined%22<p>English tenses are a nightmare...at least for me.  Do we really need such fine-grained control over tense?
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dxjones
Are you a native English speaker??

Both are correct. They are different forms of past tense, with different
meanings.

"we defined ..." The "simple past" is used for recounting past events, as when
telling a story.

"we have defined ..." The "present perfect" is used when describing a past
action that has effects on present events.

You might have learned this from your English grammar teacher, or from Google:
"wiki past tense".

\-- David Jones

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amichail
English is my third language. Anyway, it's not clear to me which is the better
choice for the tutorial sentence.

Simple past is used when there is a specific time involved. But isn't going
through the tutorial considered a specific time?

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jibiki
Either way is correct. "Have defined" sounds a little more conventional, but
it depends on context. If the simple past makes more sense to you, then you
should use it.

> Simple past is used when there is a specific time involved.

For instance "although we defined the Riemann Sum in chapter eight..." is
correct while "although we have defined the Riemann sum in chapter eight" is
probably wrong.

