Where does injection collide?

In macroeconomics, an injection is a flow of spending that enters the circular flow of income from outside the household-firm loop, so it adds to aggregate demand rather than merely recirculating existing income: the standard injections are investment, government spending, and exports. Keynes's 1936 The General Theory of Employment, Interest and Money established that such autonomous spending drives effective demand and, through the multiplier, sets the level of output and employment; the circular-flow framing later named these flows injections, set against the leakages of saving, taxation, and imports. The referent here is a monetary flow into an economy's income loop, measured in currency per period, and it has nothing to do with a function that separates points or a stream of charge crossing a junction.[1]

Unit

A flow of autonomous spending into the income loop, in currency per period

Recovery means

Not applicable

Measured by

Estimated in national accounts as investment, government expenditure, and exports, in currency per period

In semiconductor physics, carrier injection is the flow of charge carriers, electrons or holes, across a junction into a region where they are the minority type, raising their concentration above its equilibrium value. Shockley's 1949 The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors derived how a forward-biased junction injects minority carriers and how that injected current governs diode and transistor behaviour. The referent is a physical current of charge carriers crossing a boundary inside a solid, measured in amperes or carrier density, and it is unrelated to autonomous spending entering an economy or a one-to-one map between sets.[2]

Unit

A current of charge carriers crossing a junction, in amperes or carrier density

Recovery means

Injected minority carriers recombine over a characteristic lifetime and diffusion length as they return toward equilibrium

Measured by

Quantified from junction current-voltage curves and from minority-carrier lifetime and diffusion-length measurements

In mathematics, an injection, also called an injective or one-to-one function, is a map that sends distinct inputs to distinct outputs: if two inputs share an output they must be the same input. Bourbaki's Théorie des ensembles, part of the Éléments de mathématique (1954), introduced the terms injection, surjection, and bijection for these classes of maps, formalising a notion of one-to-one correspondence that reaches back to the work of Cantor and Dedekind. The referent is a structural property of a function between sets, with no unit of measure, and it bears no relation to spending flowing into an economy or carriers crossing a semiconductor junction.[3]

Unit

A property of a function between sets: distinct inputs map to distinct outputs; not measured on a scale

Recovery means

Not applicable

Measured by

Established by proof, by showing that equal outputs force equal inputs, or that the function has a left inverse