Results for: The-seed-at-zero

145 Contributions

Answered

In Numbers

Why isn't zero divided by zero either zero or one?

Consider the equation 0 times x = 0. This is true for every number x. Divide both sides by 0; we get x = 0/0. So zero divided by zero could be any number at all; it coul… (MORE)

11 people found this useful

Anand Mehta

252,204 Contributions

Statistician / Economist formerly employed in various Government Departments in the UK, freelance mathematics and statistics tutor since retiring in 2008, Fellow of the Royal Statistical Society.

Answered

In Science

What is zero and constituents on zero in mathematics?

Zero is an integer which belongs to the sets of rational, real and complex numbers. It is the additive identity which means that, for any other number n, n + 0 = n = 0 + n. T… (MORE)

3 people found this useful

Rushabh Yapuram

38,567 Contributions

B.Tech in Computer Science and Engineering

Answered

In Math and Arithmetic

What does zero to the power of zero equal?

00 = 1. This can be proved by different methods like using binomial expansion. Visit the links mentioned below to know how actually it is proved.

7 people found this useful

Hammernose

857 Contributions

Answered

In Numbers

When you divide by zero the answer is always zero?

You cannot divide by zero. Zero is special in that it does not have a multiplicative inverse. There is a reason why you did not have to memorize division by 0 tables in … (MORE)

1 person found this useful

The question and answer are locked and cannot be edited.

Mr Kbh

742,205 Contributions

Answered

In Numbers

What is zero divided by zero?

In ordinary mathematics, you may not divide by zero. It is considered undefined. Consider the two situations: For the inverse of multiplication 0/0 = a, a could be any number …to satisfy a x 0 = 0. At the same time, division of any nonzero number, a/0 = b, there is no number a such that b x 0 = a. --- In nearly every known algebraic structure, 0/0 is an undefinable term. This means that, based on the rules that govern most of the mathematical systems we use, there isn't just one, single, definable value for the term 0/0, and believe it or not, the reason for this isn't because we're dividing by zero, it's because the division relation is defined by another relation, multiplication. You see, when we talk about "divide," what we really mean is "multiply by the inverse." For example, x/y actually means, x*y-1 where y-1 is the inverse of y. The inverse of a number is defined to be the number which, when multiplied by the original number, equals one; e.g. x*x-1 = 1. Now, in the algebraic structures we're all familiar with, any number multiplied by zero is defined to be equal to zero; e.g. 0*x = 0. So, using these definitions, what does dividing by zero, which actually means multiplying by the inverse of zero, equal? In other words, x*0-1 = ? Well, to isolate x, you would need to cancel out 0-1, but how? As anyone who's taken any sort of algebra knows, the method of isolation in these cases would be to multiply 0-1 by 0 because, as stated above, x*x-1 = 1, therefore 0*0-1 = 1. But wait, didn't I also just say that 0*x = 0? That would mean that 0*0-1 = 0, which would mean that 0 = 1. That, my friends, is called a contradiction. Zero does not equal one; therefore the term 0-1 can't be defined. This answer may seem unsatisfactory to some people. There's got to be a way to work around this pesky contradiction, right? Actually, there is! In the branch of mathematics called abstract algebra, there exists an algebraic structure called a wheel which is required to have division defined everywhere within it. Therefore, in this particular algebraic structure, 0/0 must exist or else the structure isn't a wheel. But wait, 0/0 is undefined, right? How could you ever satisfy this requirement for a wheel then? That's easy; all you have to do is define it! Specifically, you give this quantity, 0/0, some specific algebraic properties, and then, if it ever comes up in an equation, you manipulate it within the equation using the properties you've given it. Isn't that convenient?! "Preposterous!" you may say. "You can't simply make something up which has no tangible or rational analogue, that's cheating!" Well my dear skeptic, may I direct your attention to the following little marvel, √(-1), otherwise known as "the imaginary number," or i. That's right, I said imaginary, as in, "doesn't exist." You see, nothing multiplied by itself in our nice little world of mathematical rationality can possibly be a negative number. Unless, of course, you define something to be as such. Then...Presto! The absurd is now reality! Let's talk about imaginary numbers for a moment. Our newly defined yet still rather imaginary friend, i, was apparently not content on simply having a nice, comfy little existence within the realm of obscure mathematics, oh no no no. It decided to defy logic and become a fairly common number; popping up all over the place, even in (you're going to love this) actual, real-life applications. For example, anyone who's ever done some form of electromagnetic wave analysis, through the fields of engineering, physics, etc., LOVES i and will gladly bow down and kiss its feet upon command (God bless ei(ωt-kr)). Why? Because of the very thoughtful relation that it's given to us known as "Euler's formula:" eiθ = cos(θ) + isin(θ). Step back a minute and look at that. The irrational, real number, e (2.71828...) exponentiated to the product of a real number, θ, and the imaginary number, i, is equal to a simple trigonometric expression involving two basic functions. In fact (you may want to sit down for this), if the value for θ happens to be π (3.14159...), another irrational, real number mind you, the trigonometric expression on the right hand side of Euler's formula reduces to exactly -1. Let's write that out: eiπ = -1. We call that "Euler's identity," although it should really be called, "THE MOST INCREDIBLE MATHEMATICAL EXPRESSION, EVER!" But enough about i, let's get back to our newest friend, 0/0. As stated earlier, the problem with 0/0 isn't the fact that we're dividing by zero, it's the fact that the division relation is defined by multiplication. Well, how do we fix that? Simple! Change the definition of divide! Instead of x/y = x*y-1, it's now going to equal x*/y, where "/" is defined as a unary operation analogous to the reciprocal operation. OK, another quick aside. A unary operator is an operator that only needs one input to work. For example, you only need one number to perform the operation of negation. For instance, negating the number 1 is simply -1. This is opposed to a binary operator. Binary operators include many of the guys we're all familiar with; like addition, multiplication, subtraction, etc. To make this clearer, consider the addition operation. It would make no sense to write 1 +. You need another number after the "+" to satisfy the operation; 1 + 2, for example, hence the term binary. So, with our trusty new unary operator "/" in hand, we're going to look at the number 0/0 again. 0/0 is no longer defined as 0*0-1 like it was before. Now, it's defined as 0*/0, and in our world, not only does /0 ≠ 0-1, but 0*x doesn't have to equal 0 either. Isn't abstraction fun?! Ok, so 0/0 is officially defined, now let's give it some properties! How about, x + 0/0 = 0/0 and x*0/0 = 0/0. Awesome! Why not go ahead and make a more general rule as well: (x + 0y)z = xz + 0y. OK! Well, we're certainly off to a good start, I'd say. I'll leave the complete derivation of the algebraic structure known as the wheel to the experts, please see the corresponding link below. I'll end this answer with a final note for those who think that this entire concept of "defining the undefined" is ridiculous. Consider the following sets of numbers: The prime numbers, P; the set of all real numbers with exactly two natural number factors. The natural numbers, N; the set of all integers greater than or equal to 0. The integers, Z; the set of all real numbers without remainders or decimals. The rational numbers, Q; the set of all real numbers that can be expressed as an integer divided by a non-zero integer. The irrational numbers, I; the set of all real numbers that aren't rational. Now consider this: The imaginary number, i, is undefined in I. The ratio pi, or π (3.14159...), is undefined in Q. The common fraction 1/2 is undefined in Z. All of the negative numbers, including -1, are undefined in N. The number 4 is undefined in P. Yet, these "undefined" numbers are hardly mysterious to us. We just broadened our definition of definable to include the "undefined" ones, and life became good again. 0/0 is not quite, but nearly, the same idea. Undefined, you cannot divide by zero. (MORE)

32 people found this useful

David Scott

14,355 Contributions

Texas A&M Electrical Eng. Degree and US Navy RADAR Tech.

Answered

In Algebra

What is zero to the zero power?

See my related link posts. There's some good information there. This is what's called an indeterminate form. There is some consensus that maybe it should be equal to 1, but … (MORE)

5 people found this useful

William6058

24 Contributions

Answered

In War and Military History

What were the zeroes?

%REPLIES% Answer Japanese fighter planes. Also a slang term for "officers". Answer Desiree--The Zeroes were … (MORE)

Penny Kaye

169,748 Contributions

"Always let your conscience be your guide.": Penny Kaye has a BS degree in Elementary Education.

Answered

In Biology

What does a seed do?

Every seed contains an embryonic plant that needs certain conditions to sprout and grow, and food for the seed to use until it forms into a plant. Seeds will germinate whe… (MORE)

Empiresj1

3,899 Contributions

Answered

In Science

What is 'zero'?

Zero is a number which is said to mean nothing. The only time it has a value is when it follows a counting number or when it comes before the counting numbers in a decimal.

Calista E

1 Contribution

Answered

In Math and Arithmetic

What is the answer to 20c plus 5 equals 5c plus 65?

20c + 5 = 5c + 65 Divide through by 5: 4c + 1 = c + 13 Subtract c from both sides: 3c + 1 = 13 Subtract 1 from both sides: 3c = 12 Divide both sides by 3: c = 4 20c + 5 = 5c … (MORE)