"It would seem that science's belief that a substance can be diluted completely out of existence is incorrect."
Not diluted out of existence, diluted out of probability. It's just math.

1 gram of phosphorus (P) contains 1.947 * 10^22 molecules of phosphorus
10 grams of water (H2O) contain 3.348 * 10^23 molecules of water

So say your dosage is 2 grams and is diluted by 10 50 times.

You have a 2 in 10^27 chance of getting one molecule of phosphorus in your dose. Expressed without exponents that's about a 1 in 1,000,000,000,000,000,000,000,000,000 chance of one molecule being in your dose. Your chances of being killed by lighting are 1 in 2,320,000.


As for the websites, they're all citing the flu pandemic and one source. I'm more interested in placebo controlled studies published in the last 10 years. The vast majority that I looked at showed homeopathy to be only slightly more or less effective than a placebo, and much less effective than commonly prescribed medicine.

Also, some of the authors of those articles actually profit off of homeopathy making them biased, as their income depends on people believing homeopathy works.