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In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.
Since the empty category is vacuously a discrete category, a terminal object can be thought of as an empty product (a product is indeed the limit of the discrete diagram {X i}, in general). Dually, an initial object is a colimit of the empty diagram 0 → C and can be thought of as an empty coproduct or categorical sum.
The empty product on numbers and most algebraic structures has the value of 1 (the identity element of multiplication), just like the empty sum has the value of 0 (the identity element of addition). However, the concept of the empty product is more general, and requires special treatment in logic, set theory, computer programming and category ...
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, =, = = This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. [1]
Second, and empty product is not the result of anything, it is something like "0!" whose value is 1, but it is not identical to 1 (or otherwise conversely "1 is an empty product", which seems a bad formulation). In short, one should make distinction between expressions and there values, and an empty product is an expression.
AAPL PE Ratio data by YCharts. PE = price-to-earnings. Compared to the S&P 500, which trades for 25.5 times trailing earnings and 22.3 times forward earnings, Apple has a premium of around 40% ...
It’s illegal to sell or buy, but casu marzu, a maggot-infested sheep milk cheese is a revered delicacy on the Italian island of Sardinia. Locals hope their unusual dairy product can shed its ...
That's probably what comes to mind when thinking about the black market -- but the illegal trade is more varied than you may think, and it also encompasses household products like maple syrup and ...