Not if we’re clever about it. The universe is infinite, so if we can find a way to travel faster than light, we only run out of resources when Heat Death happens (if it does. Mabey it wont. Hard to tell for sure. For all we know expansion could stop tomorrow. Or reverse. No way to know for sure that it will keep being like this forever). Even without FTL though, we have enough access to resources to make an amount of humans which frankly, is too large for our ape brains to comprehend.
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