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Why does the fact 0 has no multiplicative inverse still mean R is still a field?
Wiki User
∙ 12y ago
In the definition of a field it is only required of the non-zero numbers to have a multiplicative inverse.
If we want 0 to have a multiplicative inverse, and still keep the other axioms we see (for example by the easy to prove result that a*0 = 0 for all a) that 0 = 1, now if that does not contradict the axioms defining a field (some definitions allows 0 = 1), then we still get for any number x in the field that x = 1*x = 0*x = 0, so we would get a very boring field consisting of only one element.
Wiki User
∙ 12y ago
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What property is 1 times 87 equals 87?
It is the fact that 1 is the multiplicative identity.
What is mean by type constraint in DBMS?
A foreign key is a type of constraint. In this example the value in a field must be the same as some value in a defined field in another table. Example in a Customer Table you might have a Column (field) named StatusID You would define a foreign key to the table Status, field StatusID. The value in the Customer table, StatusID column must be an entry existing in the Status Table, StatusID column. There are many constraints. The fact that a column can not be NULL (Left blank) is a constraint. Defining what KIND of data, or range of data that can be entered in a column is a constraint.
Is 2 an even or odd number?
2 is an even number. I believe your confusion comes from the fact that 2 is a prime number, but it is still even. It is the only even number that is prime.
How do you simplify e raised to 8 ln x plus cos x?
By using the basic rules of exponents, plus the fact that the exponential function (e raised to some power) and the natural logarithm are inverse functions. e8 ln x + cos x = e8 ln x ecosx = e(ln x)(8) ecosx = (eln x)8 ecosx = (eln x)8 ecosx = x8 ecosx
What is it called when there is an equation that is always true?
an identity? maybe a tautology? Comment by mgately: In the field of discrete mathematics (simplified the study of logic) any expression which always evaluates to true is in fact called a tautology. While less cool sounding, an expression which always evaluates to false is just called a contradiction.
How do you determine the multiplicative inverse of a number?
The multiplicative inverse of a number is its reciprocal, meaning the multiplicative inverse of the rational number a/b is b/a. In the specialized case for integers, the multiplicative inverse of n is 1/n. This is due to the fact that a/b * b/a = 1 and n * 1/n = 1, which is the definition of a multiplicative inverse. More succinctly, to find the multiplicative inverse you "flip" the fraction or integer around to its reciprocal. This is the number that when multiplied with the original number results in a product of 1.
What are the elements in rational numbers having multiplicative inverse?
All rational numbers, with the exception of zero (0), have a multiplicative inverse. In fact, all real numbers (again, except for zero) have multiplicative inverses, though the inverses of irrational numbers are themselves irrational. Even imaginary numbers have multiplicative inverses (the multiplicative inverse of 5i is -0.2i - as you can see the inverse itself is also imaginary). Even complex numbers (the sum of an imaginary number and a real number) have multiplicative inverses (the inverse of [5i + 2] is [-5i/29 + 2/29] - similar to irrational and imaginary numbers, the inverse of a complex number is itself complex). The onlynumber, in any set of numbers, that does not have a multiplicative inverse is zero.
Which property is illustrated here 11 x 1 equals 11?
The fact that 1 is the multiplicative identity.
What is the definition of inverse property?
There are inverse properties for many things in math. Commonly, we talk about it for addition and multiplication. So for addition, take any number a, there is an additive inverse -a such that a+ (-a) =0 For example, the additive inverse of 2 is -2 since 2+ -2=0 Similiarly for multiplication, for any number a, we have some number, 1/a such that a(1/a)=1. We call 1/a the multiplicative inverse. In a more abstract sense, we look at sets of objects in math and having an inverse is one of the properties a set needs to be a group. Other things, such as functions have inverses too. In fact, the inverse property is a big topic in math.
True or false the opposite of a number is less than the number?
False. Apart from the fact that there is no such thing as an opposite. If, by opposite, you mean negative (additive inverse), then start with a negative number. The negative of this will be positive, and so greater. If by opposite you mean the reciprocal (multiplicative inverse), start with a positive number less than one or a negative number less than -1.
What does Multiplicative Identity Property look like?
The multiplicative property is the fact that any number multiplied by one will stay the same. i.e. x(1)=x
How do you find a variable in a matrix if there is no inverse?
The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.
What property would 17x1 equals 17 be?
The fact that 1 is the multiplicative identity for numbers.
Can a football player that steps out of bounds still field the ball?
no, in fact they have a penalty for that
What property is 1 times 87 equals 87?
It is the fact that 1 is the multiplicative identity.
Why when multiplying two negative numbers do you get a positive number?
The answer has to do with the fundamental properties of operations on numbers (the notions of "addition", "subtraction", "multiplication", and "division"). Each number has an "additive inverse" associated to it (a sort of "opposite" number), which when added to the original number gives zero. This is in fact the reason why the negative numbers were introduced: so that each positive number would have an additive inverse. For example, the inverse of 3 is -3, and the inverse of -3 is 3. Note that when you take the inverse of an inverse you get the same number back again: "-(-3)" means "the inverse of -3", which is 3 (because 3 is the number which, when added to -3, gives zero). To put it another way, if you change sign twice, you get back to the original sign. Now, any time you change the sign of one of the factors in a product, you change the sign of the product: (-something) × (something else) is the inverse of (something) × (something else), because when you add them (and use the fact that multiplication needs to distribute over addition), you get zero. For example, (-3) ´ (-4) is the inverse of (3) ´ (-4) because when you add them and use the distributive law, you get . (-3) ´ (-4) + (3) ´ (-4) = (-3 + 3) ´ (-4) = 0 ´ (-4) = 0 So (-3) ´ (-4) is the inverse of (3) ´ (-4) , which is itself (by similar reasoning) the inverse of 3 ´ 7. Therefore, (-3) ´ (-4) is the inverse of the inverse; in other words, the inverse of -12 in other words, 12. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
How does knowing an addition fact help with a subtraction fact?
You can do the fact backwards. ex. 3+4=7 turn it around 7-4=3 I believe it is called doing the inverse operation.
