Deriving the National Savings and Investment Identity

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As basically all such videos, this is super-fishy; substituting explanation and thought with kiddy math -and doing that kiddy math without having properly defined anything.

Just one question out of a zillion.

GDP in the first equation is presumably ALL income that is earned by all actors in the economy.
The second equation uses GDP as *private* income only.

How can the same term denote two different things? This is a hole in the argumentation the size of the milky way; and just one out of so many...

MetalMinded