Why is 1 to the infinity undefined?
Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined. In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero.
We use the terms infinity and - infinity not as a number but to say that it gets arbitrarily large. Negative infinity means that it gets arbitrarily smaller than any number you can give. so 1 - infinity = -infinity and 1 + infinity = + infinity makes sense only when looked as in this sense.
This is known as an indeterminate form, because it is unknown. One to the power infinity is unknown because infinity itself is endless.
Mathematically speaking, 1/infinity is not equal to 0. In fact, it is impossible to divide a number by infinity and get a result of 0. However, this does not mean that the value of 1/infinity is anything other than incredibly small. In practical terms, the value of 1/infinity can be thought of as being equal to zero.
1 divided by infinity:
Therefore, we consider it as zero. The larger the denominator, the closer the quotient gets to 0. So, we consider the result as 0.
. If you add one to infinity, you still have infinity; you don't have a bigger number.
Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.
tan90 is infinity and cotA=1/tanA. But, cot90=0, wheras cot90=1/tan90=1/infinity. This means that 1/ infinity=0. Cross multiplying, we get that: 1(or any other number)=0.
tells us that whenever x is close to a, f(x) is a large negative number, and as x gets closer and closer to a, the value of f(x) decreases without bound. Warning: when we say a limit =∞, technically the limit doesn't exist.
A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity).
Is infinity indeterminate or undefined?
But Infinity — Infinity is an indeterminate quantity.
The term “indeterminate” means an unknown value. The indeterminate form is a Mathematical expression that means that we cannot be able to determine the original value even after the substitution of the limits.
Infinity is not a number. Instead, it's a kind of number. You need infinite numbers to talk about and compare amounts that are unending, but some unending amounts—some infinities—are literally bigger than others.
infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655.
In terms of logarithms, the original value 0 corresponds to −∞, while the original infinite value corresponds to +∞. When we treat both possible values −∞ and +∞ as a single infinity, we thus treat the original values 0 and infinity as similar.
The value of infinity is also undefined. What is the difference between Infinity and Undefined? Undefined means, it is impossible to solve. Infinity means, it is without bound.
Let say k is any constant, k/0 = infinity, this implies 0 * infinity = k, but k is any constant. K can take any value. So as there is no fixed value equal to 0 * infinity, meaning of 0 * infinity is ambiguous. Thus, 0 * infinity is undefined.
It has no answer and is undefined since infinity is not a number, but just a concept of something very big.
The eight subsets are A, B, C, AB, AC, BC, ABC and the null set. So a higher infinity than ℵn is the set of all subsets of ℵn . ℵn+1 is equal to 2 raised to the power of ℵn. So there is no biggest infinity!
Despite having more numbers than atoms in the universe, trying to prove that your integer is bigger than anyone else's integer has continued through the centuries. The biggest number referred to regularly is a googolplex (10googol), which works out as 1010^100.
What's more than infinity?
Mathematically, if we see infinity is the unimaginable end of the number line. As no number is imagined beyond it(no real number is larger than infinity). The symbol (∞) sets the limit or unboundedness in calculus.
INFINITY IS THE BIGGEST NUMBER FOLLOWED BY OMEGA (even though they are not real numbers) thats the answer to your question.
The smallest version of infinity is aleph 0 (or aleph zero) which is equal to the sum of all the integers. Aleph 1 is 2 to the power of aleph 0. There is no mathematical concept of the largest infinite number.
Google is the word that is more common to us now, and so it is sometimes mistakenly used as a noun to refer to the number 10100. That number is a googol, so named by Milton Sirotta, the nephew of the American mathematician Edward Kasner, who was working with large numbers like 10100.
Any number times any number is a number, so let's just call any number 1. Any number times 0 equals 0 and any number times infinity equals infinity. In this way, they are similar to the square root of -1. As long as there are an even number, you get a real number.
The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1.
So 1 || 0 is 1 , not true ; and false || 0 is 0 (even though 0 is falsey). So for the same reason, Infinity || true is Infinity , not true .
A limit is undefined whenever the function does not approach a finite value.
Infinity is not a real number. It's a mathematical concept meant to represent a really large value that can't actually be reached. In terms of solutions of limits, it means that the equation you are taking the limit of will go in that direction forever.
In short, the limit does not exist if there is a lack of continuity in the neighbourhood about the value of interest. Recall that there doesn't need to be continuity at the value of interest, just the neighbourhood is required.
Is 0 ∞ an indeterminate form?
Limits of the Indeterminate Forms 00 and ∞∞ . A limit of a quotient limx→af(x)g(x) lim x → a f ( x ) g ( x ) is said to be an indeterminate form of the type 00 if both f(x)→0 f ( x ) → 0 and g(x)→0 g ( x ) → 0 as x→a.
Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form.
In mathematics, undefined means a term that is mathematically inexpressible, or without meaning. Anything divided by zero is considered undefined by the rules of mathematics.
No Finite Value Limits
Since infinity is not a finite value, the limit of the function as x approaches 1 is undefined.
When something is undefined, this means that there are no solutions. However, when something in indeterminate, this means that there are infinitely many solutions to the question. Again, zero and infinity are the root to a lot of mathematics, including the difference between these two words.
Answer: Infinity to the power of zero is equal to one.
Let's understand the solution in detail. Explanation: ∞0 is an indeterminate form, that is, the value can't be determined exactly.
In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity. Similarly, expressions like 0/0 are undefined.
We say that 00 is an indeterminate form because a limit of that form can take any value:limy→0xyy=x, for any real number x. On the other hand, a limit of the type 10 cannot take any value.
Some numbers come after googolplex, and we have named them too. Skewes' number is one of the larger numbers than even a googolplex. This number was developed by mathematician Stanley Skewes and named after him.
How much is a googolplex?
A googol is 10 to the 100th power, which is 1 followed by 100 zeros. While this is an unimaginably large number, there's still an infinite quantity of larger numbers. One such number is googolplex, which is 10 to the power of a googol, or 1 followed by a googol of zeros.
In practice, the supposed existence of actual infinity in nature is questionable. It seems that because we have a symbol (∞) to represent infinity, many physicists believe its appearance in a theory is no big deal: it is part of the natural order. But this is not the case.
: The ideal point at the right end of the number line. With this definition, there is nothing (meaning: no real numbers) larger than infinity.
Infinity goes on forever, so sometimes space, numbers, and other things are said to be 'infinite', because they never come to a stop. Infinity is not really an ordinary number, but it is sometimes used as one. Infinity often says how many there is of something, instead of how big something is.
About Infinity
Similarly, there is a concept called negative infinity, which is less than any real number. The symbol “-∞” is used to denote negative infinity.
So that's the answer to your question. If infinity plus one is infinity, the only number that could be just before infinity is also infinity!
No matter how much you take from infinity, you can't set it back to zero unless it works in one of two ways. GER's power is a multiplication reset. When Act 4 attacks it, they just pass through each other and nothing happens to either party, and nothing will ever happen. Stalemate.
In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity. Similarly, expressions like 0/0 are undefined. But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate.
Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.
Infinity is not a real number and is only used as a representation for an extremely large real number. Dividing 1 by infinity is equal to zero. In general, any real number divided by infinity is zero, and the quotient of nonzero real numbers that divide infinity is infinity.
Why the sum to infinity does not exist?
The sum to infinity only exists if -1<r<1. If the common ratio is outside of this range, then the series will diverge and the sum to infinity will not exist. If |r|<1, the sequence will converge to the sum to infinity given by S∞=a/(1-r). A convergent geometric series is one in which the terms get smaller and smaller.
It is undefined. When infinity is multiplied with any number, answer will be zero. however 0*∞ is undefined.
So ! undefined is true because undefined implicitly converts to false , and then ! negates it. Collectively, those values (and false ) are called falsy values.
Infinity has no end
So we imagine traveling on and on, trying hard to get there, but that is not actually infinity. So don't think like that (it just hurts your brain!). Just think "endless", or "boundless". If there is no reason something should stop, then it is infinite.
The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite.
Not only is the infinity of decimals bigger than that of the counting numbers – there is no biggest infinity. Beyond infinity is another infinity, and beyond that is yet another… and even after you've reached an infinity of infinities, there's still another infinity beyond that.
A rational number is a fraction with an integer on top or bottom. There are a lot of them. In fact, there are infinitely many of them between 0 and 1. No matter how close you look, there are always infinitely more of rational numbers squeezed into that gap.
Never. There are an infinite number of different values for infinity, and some are infinitely larger than others, and some are infinitely smaller than others. Is infinity divided by infinity = 1?
Let say k is any constant, k/0 = infinity, this implies 0 * infinity = k, but k is any constant. K can take any value. So as there is no fixed value equal to 0 * infinity, meaning of 0 * infinity is ambiguous. Thus, 0 * infinity is undefined.
"Actual infinity does not exist. What we call infinite is only the endless possibility of creating new objects no matter how many exist already. " H. Poincar e (1854-1912). "Every infinity is potential." Aristotle (384 BC – 322 BC) "Actual infinity exists" Geprge Cantor (1845-1918) It is a very controversial question.