When is a sample size too large? 
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*At what point exactly is a sample size considered "really large"?

*In hypothesis testing, do small differences become consistently significant when n is 100,000?

*What about 100,001?

*Is there a definite limit between a large and a small sample size?

An example in R or a published article would also be helpful!

A sample is too large when it costs too much. Too much time, too much money, too much effort, too many graduate students, or too many slithy toves. From the point of view of determining the properties of the statistical population being sampled, more is better.
Some of the concerns about 'overly large' samples concern a low p-value being taken as a sign of importance or real-world 'significance'. Avoid that by paying attention to the magnitude of the effect observed. Always report the effect size and always scale it relative to real world considerations.
Other concerns about 'overly large' samples come from the idea that in a repeated testing (sequential testing) situation, sampling until the p-value is smaller than any arbitrary value will always stop with the low p-value, in theory. In practice that is not true because in the real world sampling is constrained by time, money, effort, etc. And anyway, even if you did stop with a false positive low p-value from such a protocol you would most often be protected from real world mistake by paying attention to the previous paragraph.
