ELI5 Schrödinger's Cat - is the cat both dead and alive and why does it matter in quantum mechanics?

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Explain Schrödinger's Cat in simple terms. Why did Erwin Schrödinger propose this thought experiment in the first place? What was Schrödinger trying to argue against with his cat example? Which other scientist inspired Schrödinger to devise the cat?

... we explain like I'm five

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