I have 10 in my pocket now. Let 10 = x. If I invest 10, I invest x. If I didn't invest the 10, how much would I have? 10, which is x.
What I invest = 10
What would I have if I didn't invest? the 10 in my pocket.
Is 10 = 10 not the same quantity? Is there something wrong with this assumption? Sorry I'm not getting where you're coming from.
Wrong. If you invest 10
in something that increases the value of the currency (ie, something that makes goods cheaper, such as a more efficient manufacturing process), then that 10 (in nominal terms) is suddenly worth more than 10 in real terms, eg, if the value of the currency doubles, it is worth 20 in real terms. Let us postulate two alternate universes, Alternate Universe A, in which your investment increased the value of the currency, and Alternate Universe B, in which you didn't make that investment, and so the currency did not increase in value. $10 from Alternate Universe A are certainly not the same as $10 from Alternate Universe B if dollars from A are worth more than dollars from B. I honestly can't help you if can't figure that out.