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The sun expanding will not be the cause of humanity going extinct. Most species go extinct after about 2 million years. Things change, climate changes, etc. Homo Sapians have been around for about 200K years. We depend entirely on our modern society to survive. Even survivalists have sophisticated knives, guns, materials, and technology to help them survive. How many of us could really survive given a few scraps of clothing and whatever rocks we could gather? And it would take very very little to destroy our modern civilization. One supervolcanoe, one semi-massive meteor, the next ice age, and society is destroyed. These things happen on the order of every few million years or so. Humanity has never experienced any of these on a major, major scale - but we will. And that doesn't even account for the fact that society is consuming non-renewable resources at a rate far greater than can be sustained. If we destroy a critical mass of rainforest, or consume the world's oil supply, or simply cannot get fresh water and food, society could collapse. Our distant ancestors had pristine land filled with animals to hunt and plants to gather, and had tribal knowledge to survive without technology. Today, it's entirely possible that we would collapse to the point of extinction.
The point is, extinction events happen on a time scale that exceeds the homo sapian existance. But they do happen. And on the order of hundreds of millions of years, even the Earth may change. Oxygen levels could drop, or raise, to a point where humanity cannot breathe the air. It happened at the end of the Triassic, it could happen again.
If we ever get the technological ability to live off world, on Mars or the Moon, then we'd have a much greater chance at success. These world are geologically dead, which means the environments do not change. However, that technology and the economic means to live off-world without depending on the home planet is still a very long way away, if it ever comes. Certainly not in your grandchildren's lives.
The point is, extinction events happen on a time scale that exceeds the homo sapian existance. But they do happen. And on the order of hundreds of millions of years, even the Earth may change. Oxygen levels could drop, or raise, to a point where humanity cannot breathe the air. It happened at the end of the Triassic, it could happen again.
If we ever get the technological ability to live off world, on Mars or the Moon, then we'd have a much greater chance at success. These world are geologically dead, which means the environments do not change. However, that technology and the economic means to live off-world without depending on the home planet is still a very long way away, if it ever comes. Certainly not in your grandchildren's lives.