This is not something I expect humans
to achieve anytime soon, or ever... And that's because of political, legal and financial reasons, NOT because of engineering and technological limitations.

There are 6 billion people on the Earth.
Imagine housing 99-percent, or 99.99 percent of them in ONE humungous skyscraper? Actually in one huge cubic
apartment building, not a vertical- rectangular structure.

OK!
Here are some numbers.
If you build a cubic apartment building
that's 1000ft x 1000ft x 1000ft, it could house well over 10,000 people in comfort.

If you scale that up by 10^3, so that you have a two-mile high, two-mile wide by two-mile breadth cubic apartment
building, you can house over 10-million people in comfort in it [That's about
the population of Texas]

Now scale that up another 10^3, you're talking about a 20-mile high, by 20 x 20 mile breadth and width cubic apartment building, that can house 10 billion people...more than all the people on Earth today.

The upper 18-miles of structure would be sealed air-tight with 'bullet-proof' type glass and shielding against ultra-violet light.
Distributing electricity, and optic-fiber communications links throughout the building would be no real problem...

Air circulation and force-pumping of same [expecially into and throughout the
top 18-miles of the building] would be
problematic but NOT UNFEASIBLE...

Pumping water throughout such a building, expecially to the top floors,
twenty miles up, would present a GREAT ENGINEERING CHALLENGE, something that would tax present technology to the limit...But it's doable.

The huge building would need elevators.
Lots of them....That's definitely another GREAT ENGINEERING CHALLENGE...
[One solution may be the use of differences in air-pressure throughout the height of the building to vertically convey passengers and freight
in the elevator-shafts. Ex: If an elevator 'box' is morphed into a huge airtight cylindrical-piston inside an airtight tube. As the piston-shaped elevator 'box' comes down inside the airtight elevator-tube it compresses
the air below, much like a spring,
storing energy for the ascent up later...so much for the need of cables...Electro-magnetic shunt-motors
may also serve as a substitute for elevator cables, too.

Why only 99 or 99.99 percent of
Earth's population living in such a building?...

ANSWER: You need fishers,
farmers, ranchers, orchard harvesters to provide you the food available
in your huge apartment building's numerous supermarkets and you need miners, quarrymen, foresters, etc., to provide the nearby "industrial-park" with raw materials. And the shippers and teamsters to deliver it all. They have to live outside the building, near the resources, at least part of the year...

What about the threat of an epidemic,
either from a natural source, or bioterrorism, inside such a building?

ANSWER: No real problem!...Hygiene will be strictly enforced....Air and water will be closely monitored and repeatedly tested, treated and filtered...Medical practitioners and clinics will be available on every floor and wing of the building. And at the first sign of an outbreak, quarantine and treatment measures will be rigorously carried out.

What about the threat of hurricanes,
earthquakes, volcanoes, etc.?

ANSWER: You can't protect against every contingency, but the huge building
will be able to resist hurricanes, and it can be built in minimal geologically
active zones: Ex: Texas, Australia, North Africa, etc...

What about crime?

ANSWER: What about it? There will be police on every floor. There will be jails and judges and lawyers, too.

What about sports facilities? Parks & zoos? Political, ethnic and social differences and petty parochial rivalries, suspicions and jealousies?

ANSWERS: (1) Stadiums and playing fields can be build inside or outside the huge apartment building,
(2) No problem.
(3) Yes! There will be politicians
running the show, administering the building, and disagreeing with each other in numerous languages.
Yes! There will be ethnic, religious,
linguistic and cultural differences
[Anybody been to New York City, or Toronto, lately?]. Everybody will name
their floors or building wings after their heroes...And they'll fly or drape
their flags...Nothing new there.

Fire?

ANSWER: No problem! There will be
firefighters on each floor. And the building will have sprinklers and alarms
and excellent fire codes.

Horizontal transportation inside the building?

ANSWER: Electric shunt-cars and electric-powered mass transit on each floor.

How much is the rent?

ANSWER: Good question! I don't know.

cheers.

Jacob