No, a number over zero is not considered infinity. Infinity is often defined as an unbounded or infinite quantity that is far greater than any number. Though numbers over zero can be considered very large, they are not infinite and are always bound to a finite number.
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What is a number over 0?
A number over 0, also known as a positive number, is any number greater than zero. Positive numbers can include integers such as 1, 2, 3, and decimals such as 0. 5, 0. 75, etc. A positive number has no sign and is greater than zero and can be written with a + symbol in front of the number, such as +1, +2, and so on.
Positive numbers are an important concept in mathematics and can be used for a variety of calculations including addition, subtraction, multiplication, division and more. They are also used to represent measurements and to compare values.
Why is 1 divided by 0 undefined?
Division by zero is undefined because it is impossible to meaningfully divide something by zero. As division is a type of operation that is used to compare two values, if one of those values is zero then the result of the division cannot be determined.
As there is no way to numerically calculate a number when one of the values is zero, the result would have to be undefined.
Furthermore, the laws of algebra dictate that for a/b to be equal to some number it must be true that a=bx, where x is some real number. As zero multiplied by any number will always equal zero, it follows that if b equals zero in a/b, then a must equal zero as well.
This means that whatever the value of a is, the answer to a/0 will always be zero. This is impossible, as any number divided by zero should result in an infinitely large number for the answer. Therefore, 1 divided by 0 is inherently undefined.
What is the limit of 1 over 0?
The limit of 1/0 is undefined because division by 0 is undefined. The definition of a limit is the value that a function approaches as the input of the function approaches a certain value. The input of 1/0 is 0, but dividing by 0 is not allowed, so the limit of 1/0 is undefined.
How do you know if a limit does not exist?
When determining if a limit does not exist, you can generally use either a graphical approach or an algebraic approach. Graphically, if you are examining the limit at a particular point, and the graph is approaching different values from either side of that point, then the limit does not exist; this is often referred to as the “zigzag” test.
Algebraically, if the left hand limit and the right hand limit are not equal to each other, then the limit does not exist. Additionally, if you have an undefined expression at the limit, such as a division by zero or a square root of a negative number, then the limit also does not exist.
Using these approaches, one can usually easily determine whether or not a limit exists.
At what point does a limit not exist?
A limit does not exist at a point when the function is discontinuous there. This means that the limit of the function does not approach a single finite value as the independent variable approaches the point.
In other words, the limit of the function does not approach a single value as the independent variable approaches the point from either side. This can occur in a variety of ways, such as when the function has a vertical asymptote or a “hole” (where its graph jumps over a point without touching it).
Additionally, a limit can fail to exist if the left-hand and right-hand limits both approach different values, or if the left-hand or right-hand limit does not exist at all.
Can you have 0 in the numerator for limits?
Yes, you can have 0 in the numerator of a limit expression. Limits are all about understanding what the function is “trying to do” as the independent variable approaches a certain value. Whether the numerator is 0 or some other value is not as important as understanding how it behaves as it approaches the value in question.
For example, in the limit expression “lim x→ 0 (1 / x)” the numerator is 1, so that expression could be rewritten as “lim x→ 0 1/x” As the value of x approaches 0, the “1/x” term evaluates to infinity.
That’s why the limit expression can be rewritten without the numerator, since the behavior is the same regardless.
However, if instead the numerator was 0, then the “1/x” expression would evaluate to 0 regardless of the value of x. So if the limit expression was “lim x → 0 (0 / x)” it can be rewritten as “lim x → 0 0”.
Since the numerator is 0, the limit expression will always evaluate to 0 regardless of the value of x.
Can a limit of a function be 0?
Yes, a limit of a function can be 0. A limit of a function is a value that a function approaches as it gets infinitely close to a certain input. If a function is continuous, it can approach the value of 0.
Even if the function only reaches 0 in specific start and end points, the limit could still be 0. For example, the function f(x) = |x| has a limit of 0 as x approaches 0, even though the function only equals 0 for the point x = 0 itself.
Therefore, it is possible for the limit of a function to be 0.
What is infinity raised to infinity?
Infinity raised to infinity is an expression that, while mathematically meaningful, is often difficult to assign a precise numerical value to. Generally speaking, it can be understood to mean a very large number, often considered to be larger than any finite number that could be expressible.
Some definitions of infinity, such as Aleph-zero and higher order infinities, suggest that as infinity is raised to ever greater powers, the resulting numbers become increasingly large, but never actually reach true infinity.
Symbolically, infinity raised to infinity is often expressed as ∞^∞.
What is bigger than infinity?
It is impossible to answer this question with a definitive answer because infinity is not something that mathematically exists in a set form. Infinity is an abstract concept and it is used to refer to something that has no definite end or limit.
Therefore, anything that is bigger than infinity would fundamentally be impossible to measure or quantify.
Why is infinity 1 0?
Infinity (∞) is a concept that cannot be fully grasped by the human mind and is therefore often referred to as “unbounded” or “limitless”. In mathematics, infinity is a number that is greater than any other number and it is represented by the symbol ∞.
In certain special cases, infinity can be assigned a numerical value of 1 0, where 0 denotes the absence of any finite quantity.
When it comes to certain special equations or calculations, assigning infinity a numerical value of 1 0 allows the equations and calculations to be solved within specific parameters, as infinity would normally be too large a number to be able to solve equations with.
For example, when calculating the area of a circle, the area is calculated from its radius squared multiplied by pi (π). Since the radius can never reach infinity, assigning the numerical value of 1 0 for infinity allows for calculations to be made for circles of any size, as the infinite number of possible radii is then limited to 1 0.
This concept of infinity being assigned a numerical value of 1 0 can also be seen in the concept of limits. In mathematics and calculus, the concept of limits is used to determine the behavior of a function when it approaches a certain number.
If a function is approaching an infinity value, assigning a numerical value of 1 0 allows derivations and calculations to be done on the function as it approaches that value.
In summary, assigning infinity the numerical value of 1 0 in certain special cases allows equations and calculations to be solvable and manageable, as infinity itself cannot be comprehended by the human mind, and is just too large of a number to be able to solve equations.
