Apparently the set theory I learned in my precalc was actually naive set theory, why is it called that way?

>“You mean you think in hindsight the lockdowns and the social distancing and the mask mandates and all the other things we did were worse than Covid?
>“Easily. Easily. Especially for kids. But they don’t want to hear that. They won’t quote me when I say that.”
>“They don’t want to talk about how this has ravaged children. They don’t want to talk about mental health. They don’t want to talk about anything that doesn’t fit the (moving hands together) constraints. The damage due to alcoholism has been beyond anything I’ve seen.”
>“The amount of liver damage we’ve seen at this hospital would blow your mind. They called alcohol an ‘essential service’ and we, of course, have delivery service now. The number of people who *will* die in the coming years due to damage to their livers will be astonishing. We don’t see these numbers yet, but a lot of people are going to die prematurely in the coming years because they used alcoholism to cope with lockdowns. That’s just one example. There are many. They don’t want to talk about it.”

What do you think about the consequences the lockdowns and isolation will have on people?

Thorium: Epic new technology or cringeworthy meme?

Hah!
It's poetry in motion
She turned her tender eyes to me
As deep as any ocean
As sweet as any harmony

Mmm - but she blinded me with science
"She blinded me with science!"
And failed me in biology
Yeah-eah!

Huh-huh!
When I'm dancing close to her
(Blinding me with science - science!)
"Science!"
I can smell the chemicals
(Blinding me with science - science!)
"Science!"

"Science!"
Mmm now but it's poetry in motion
And when she turned her eyes to me
As deep as any ocean
As sweet as any harmony

Mmm - but she blinded me with science
"She blinded me with science!"
And failed me in geometry
Huh-huh-huh-huh-huh

When she's dancing next to me
(Blinding me with science - science!)
"Science!"
Mmm-mmm, mmm-mmm, mmm
I can hear machinery
(Blinding me with science - science!)
"Science!"

Hah!
It's poetry in motion
And now she's making love to me
The spheres are in commotion
The elements in harmony

She blinded me with science
"She blinded me with science!"
And hit me with technology
Huh-huh-huh-huh-huh

"Good heavens Miss Sakamoto - you're beautiful!"

I - I don't believe it!
There she goes again!
She's tidied up, and I can't find anything!
All my tubes and wires
And careful notes
And antiquated notions

But - it's poetry in motion
And when she turned her eyes to me
As deep as any ocean
As sweet as any harmony

Uhhh - but she blinded me with science
"She blinded me with - with science!"
She blinded me with...
Huh-huh-huh-huh-huh

Is is possible that suicidal people, just free willed there suicide to make everyone else an bad day on purpose?

how to do criticality experiment at home?

Can we prove reincarnation is real?

There's multiple records of childs borns with legit previous life experiences that were confirmed as legit memories.

I have a crush on a guy despite being straight. What is the scientific explanation for this?

I saw a thread earlier that mentioned Collatz, and as I have been working on that for some time now, I feel that I can share my work that I feel will be crucial towards any conceivable proof of Collatz. I lost my original notes since I've moved residences, however, this is an anecdote important enough that I've committed to memory.

There are infinitely many solutions to $4^{k} = 3n + 1$ such that k is a positive integer, and n is a positive integer (n is also odd by definition). For each value of k, there exists a value n that satisfies the equation. Presuming Collatz to be correct would imply that any value n that is a natural counting number will eventually reach a power of 4, and since 4 is a power of 2, the sequence will collapse to the trivial cycle.

Can somebody explain where the ? came from and why (a_n)^1/n*r<1-? and why does that mean convergence?