> Although snowflakes are all the same on an atomic level (they are all made of the same hydrogen and oxygen atoms), it is almost impossible for two snowflakes to form complicated designs in exactly the same way. While snowflakes can be sorted into about forty categories, scientists estimate that there are up to 10^158 snowflake possibilities. (That’s 10^70 times more designs than there are atoms in the universe!)
I don't think this is what people are talking about when they say "no two snowflakes are the same". Treated this way, no two of anything could ever be the same. Why even bother having the word "same"?
We can’t really confirm it for anything. It’s all up to the axioms you choose. Equally reasonable ones would have them all distinct, uniform, and everything in between.