The problem is, that’s exactly what the … is for. It is a little weird to our heads, granted, but it does allow the conversion. 0.33 is not the same thing as 0.333… The first is close to one third. The second one is one third. It’s how we express things as a decimal that don’t cleanly map to base ten. It may look funky, but it works.
???
Not sure what you’re aiming for. It proves that the setup works, I suppose.
x = 0.555…
10x = 5.555…
10x = 5 + 0.555…
10x = 5+x
9x = 5
x = 5/9
5/9 = 0.555…
So it shows that this approach will indeed provide a result for x that matches what x is supposed to be.
Hopefully it helped?
The way I think of it, there is no subtraction, and there is no division. Or square roots.
There is the singular layer of operations (the adding/subtracting layer which I think of as counting, multiplying/dividing layer which I think of as grouping, etc).
Everything within that layer is fundamentally the same thing. But we just have multiple ways of saying it.
Partly because teaching kids negative numbers is harder than subtraction, and thinking of fractions is hard enough without thinking of it as a representative process of relationships via multiplication.
Again, just how my brain does things. I’m not a mathematician or anything, but I’m pretty decent at regular math.
Oh, no denying that at all. It is a problem, especially in aggregate.
When looking at the big picture, those rotten apples really do spoil the bunch and it can be depressing.
But also people can take that big picture awareness of problems and hate on people a little universally. Saying things like humanity is awful and a plague on the earth and maybe shouldn’t exist. There’s absolutely reason to see things that way.
But we are also a species that dolphins can approach for help when they’re injured. Or that will fight tooth and nail to help a wild creature. Or who will sacrifice their own well-being, not just for friends and family, but for strangers. Who will take other creatures, like dogs, into our homes and hearts and love them with all we have.
We can suck as a species, absolutely. We need to fix it. But it’s important to remember the joys of humanity, and not just the failures. Both are extreme, for we are a rather extreme species!
It really is a matter of perspective.
You’re saying that 10% of the population being awful means that a “huge number” are deeply broken.
So then 90% are being good! Mind, it doesn’t take too many assholes to wreck things for everyone, but it is nice that the majority of folks really are trying to do their best. A sizeable majority, even!
I’m now envisioning a car wrecking its way into a house, and then trying to make cat sounds with its engine and stuff (the meows would be kinda hard, but whining would be easy enough) at the door of the restroom, and then the tires just squeal as it zooms away as the person opens the restroom door. I’m envisioning the sheer, overwhelming perplexity on their face.
I’m completely cracking up over this image. It’s amazing.