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What is the difference between the zero property of multiplication and the identity property of addition?

Usually, the identity of addition property is defined to be an axiom (which only specifies the existence of zero, not uniqueness), and the zero property of multiplication is a consequence of existence of zero, existence of an additive inverse, distributivity of multiplication over addition and associativity of addition. Proof of 0 * a = 0: 0 * a = (0 + 0) * a [additive identity] 0 * a = 0 * a + 0 * a [distributivity of multiplication over addition] 0 * a + (-(0 * a)) = (0 * a + 0 * a) + (-(0 * a)) [existence of additive inverse] 0 = (0 * a + 0 * a) + (-(0 * a)) [property of additive inverses] 0 = 0 * a + (0 * a + (-(0 * a))) [associativity of addition] 0 = 0 * a + 0 [property of additive inverses] 0 = 0 * a [additive identity] A similar proof works for a * 0 = 0 (with the other distributive law if commutativity of multiplication is not assumed).


What is the difference between primary colors and additive colors?

#1 primary colors make additive colors


What is the difference between evaluation and comparison?

Comparison happens after evaluation. Without evaluation ther is no comparison


Difference between additive model and multiplicative model in time series?

answer it


Comparison between inundation and flooding?

what is the difference between flood & inundation


What is the comparison to 76.51and 76.15?

There is a difference of 0.36 between them.


What are the comparison difference between UK and Turkey?

A couple of letters.


What is comparison-contrast?

Contrast is to find difference between two things while comparison is to make difference between two things including positive and negative points to conclude which is better .


How do you get comparison and contrast?

what is the definition of comparison and contrast writing


What is the difference between the expression s-7 and 7-s?

One is the additive inverse of the other.


What is different between multiplication and division of vector by a number?

There is no real difference between the two operations. Division by a scalar (a number) is the same as multiplication by its reciprocal. Thus, division by 14 is the same as multiplication by (1/14).


What is the difference between additive identity and additive inverse?

The additive inverse is a number subtracted it's self is 0: x + (-x) = 0 The additive identity is a number plus/minus 0 is itself: x +/- 0 = x They're very similar