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What is the difference between the phrase as I understand it and as far as I understand it? For example:
As I understand it, you passed the exam in the end.
As far as I understand it, you passed the exam in the end.
I feel that there is a difference, but I cannot pinpoint it.
Often such phrases are merely padding, giving the speaker time to formulate their thoughts, the phrases are not intended to be parsed in detail.
In the same way, "You know what I mean?" is often not really a quwstion
If we do look at the meaning, in both cases the speaker is expressing at least a formal openness to correction. Tone of voice and emphasis may colour the degree of that openness.
Please correct me if I'm wrong
can shade into
Please correct me if I'm wrong (but I'm pretty darn sure I'm right, and in fact I'd hate to be corrected)
The second phrase has more of an expression of uncertainty, in that the understanding expressed has limits (it only reaches so far) and therefore there may be additional information that will modify the opinion.
Note: The examples you give of a rather binary result (the exam was passed) may not be the best context for these kind of nuances. It might be more interesting to look at discussions of more complex or graduated issues.
