You ever see a dog that’s got its leash tangled the long way round a table leg, and it just cannot grasp what the problem is or how to fix it? It can see all the components laid out in front of it, but it’s never going to make the connection.
Obviously some dog breeds are smarter than others, ditto individual dogs - but you get the concept.
Is there an equivalent for humans? What ridiculously simple concept would have aliens facetentacling as they see us stumble around and utterly fail to reason about it?
There’s lots of proofs for this but this is the simplest one.
.333… = 1/3
.333… • 3 = .999…
1/3 • 3 = 1
Therefore .999… = 1
Why is .333 being treated the same as a third?
You could have .3 of 2.7 and that wouldn’t be a third. So I don’t see why .3 times 3 would be anything other than 0.9?
.333… Not .333
The “…” Here represents an infinitely repeating number.
In this context 1/3 = .333…
Just pretend I added dots. But that still doesn’t change anything?
Imagine a pizza, I can divide that pizza into halves, thirds, quarters, etc. because conceptually they represent splitting a defined thing into chunks that are the sum of its whole. 1/3 can exist in this world of finites.
0.333… is unending. I can’t have 0.333… of a pizza, because 0.333… is a number and that makes as much sense as saying I’ll have 2.8 pizza. Do I mean 2.8 times a pizza, 2.8% of one? Etc.
0.333… represents 0.3 repeating, which has an infinite number of 3s and is exactly equal to 1/3.
I don’t agree that they are the same.
It’s just that the difference is infinitely small
