system
A chat on subreddit /r/PoliticalCompassMemes
human
&gt;China can eventually fling enough bodies at Taiwan to overwhelm their defenses even with horrific losses. There is no realistic amount of men they are unwilling to sacrifice.

Naval landing troops are carried by boats and there's a finite supply of those, but an effectively inexhaustible supply of artillery shells and missiles.

1940s china wasn't able to do it, despite horrific losses, and they were very willing to kill as many of their soldiers as necessary, as evidenced in Korea.
gpt
While it is true the supply of amphibious transports is limited, so is the supply of Taiwanese defenses including but not limited to: airfields, vehicles, aircraft, infrastructure, ammunition, infantry, costal defense gun positions, artillery batteries, bunkers, and factories. 

China can bomb the ever living shit out of anything Taiwan has before any landing. Even with US supplied air defences, that will slow it down, not stop it. And there is *not* an unlimited supply of artillery or ammunition. Every time an artillery battery fires, it reveals itself, leaving it vulnerable to attack from counter-battery fire from naval vessels, air assets, and even missles launched from the mainland. China will be able to destoy them, and new ones will not be able to be manufactured until after the war is over. Destoyed railroads and cratered highways will complicate moving supplies, ammunition or troops where they are needed. Missle launch sites can be destroyed. 

Look, I am the last thing from some kinda Chinese military simp; I have little doubt that we'd kick the piss out of China in anything but perhaps a small skirmish that never escalates into a full war. But Taiwan simply does not have sufficient resources, of any kind, be they population, muntitions, or hardware, to witstand invasion indefinitely from anyone, much less one of the largest countries on Earth. Even with the advantages of being an island. That's why part of the aid we are giving to Taiwan is training in guerrilla warfare and insurgency: we know there is a real risk organized resistance might cease before we can get any significant reinforcements over there. 

Here is what an invasion scenario might look like: China mobilizes it's fleet to surround the island. It begins launching both ground and air based missles and aircraft sorties with the objective of destoying the Taiwanese anti-air defenses. Taiwan fights valiantly, sinking many cheap ships (China pulls their important vessels out of range, because they have a whole ocean to maneuver around) and downing many Chinese planes, and intercepting many missiles. However, China is able destroy Taiwanese anti-air and anti-ship capabilities even though losses are heavy. Now that the costal waters and airways are secure, China flies continous sorties to level any costal defenses. The invasion begins while suppourting assets focus on destroying artillery, fortifications, armored vehicles, and infantry, in that order. Chinese losses on the beaches are heavy, but few Taiwanese guns are able to fire more than a few times before being silenced in a counter strike. Once Chinese forces begin to secure the beacheads, it is the begining of the end. Despite inflicting upwards of 3-1 casualties, Chinese artillery, aircraft, missiles, and numbers give the Chinese enough of an advantage to overcome the spirited fight put up by the defenders. So the question is this: Can the US Navy (7th out of Japan and probably also 5th fleet from the Gulf) arrive in time to kick China out of the sea, trap any Chinese troops that have landed, and prevent more from arriving? Can US troops get to Taiwan before organized resistance ceases? 

I think you have understimated how costly inflicting horrendus losses on China will be for Taiwan. It will be a bloodbath, but China can keep it up for a lot longer.