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And yet, people confuse the two.

"There is no evidence for life elsewhere in the universe."

"So you believe we're alone in the universe?"

"Absence of evidence is not evidence of absence"
Absence of evidence after you've spent a lot of effort looking for evidence IS evidence of no X.

After doing a lot of research into homeopathy we are now very confident that it does not work and cannot work.

Agreed.

It is also often a very bold claim to say "There is *no* evidence for X." The cases where you can truly say that are rare compared to how easily people (esp. non-experts) will say it. More often, it's more accurate to say, "I don't believe the arguments for X or evidence of X."

How do I downvote this? You went to high school and learned the definition of a null hypothesis?
Exact reason why there is no actual consistent non-contradictory atheism view, only agnosticism and theism can be logically sound.