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Since there's a bunch of people shitting back and forth about what came first and whatnot, let's review really quick.
The original Pokemon games (Red and Green) came out in Japan on February 27th, 1996. The first Tamagotchi toys came out in Japan on November 23rd, 1996. The first Digimon V-pets came out in Japan on June 26th, 1997, a little over half a year after Tamagotchi.
Here's where things get interesting though. Tamagotchi came to the United States in June 1997, and Digimon came shortly after around the holiday season. But Pokemon Red and Blue came out on September 28th, 1998.
So while Pokemon came first in Japan, Tamagotchi and Digimon came first in America.
And for the record, yes, Tamagotchi was the first virtual pet. Nano Pets and GigaPets were born from other companies taking advantage of Bandai not being able to meet demand for Tamagotchi. This is why the brands are always confused with each other in the US; parents would struggle to find a legitimate Tamagotchi and just settle for the next best thing.
But Nanos and Gigas were fucking awful, souring the reputation of not just Tamagotchi, but virtual pets as a whole, which became a huge fucking problem for Bandai when they finally started ramping up Tamagotchi production. If Bandai hadn't been able to successfully spin off Digimon into an anime and video game franchise and net some key toy licenses, they would've gone under around the time Tamagotchi was discontinued.