0/0 , ∞/∞, ∞ - ∞ , 0x∞ , ∞0 , 00 , 1^∞. Infinity ∞ is NOT a real number it used to solve problems related to (limits) for some value that goes to large positive and negative unbounded values; they are familiar with L'hopital rule. To understand ∞ we need some topology and compactification of R.
Infinity is a concept, not a real number. Something without a beginning or an end. It is impossible to quantify infinity. Infinity cannot be measured.
Infinity is a "real" and useful concept. However, infinity is not a member of the mathematically defined set of "real numbers" and, therefore, it is not a number on the real number line.
Infinity is best described as a concept or an idea, rather than a concrete number. In math, infinity is often treated as a number in that it can be used to count or measure things, but it is not considered a natural or a real number.
Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result. Even in maths, the idea that something could have no limit is paradoxical. For example, there is no largest counting number nor is there a biggest odd or even number.
Georg Cantor was the first to fully address such an abstract concept, and he did it by developing set theory, which led him to the surprising conclusion that there are infinities of different sizes.
As no number is imagined beyond it(no real number is larger than infinity). The symbol (∞) sets the limit or unboundedness in calculus. But in cardinal and ordinal numbers there are other bigger infinities which are surreal numbers.
Addition Property. If any number is added to infinity, the sum is also equal to infinity. ∞ + ∞ = ∞
It is impossible for infinity subtracted from infinity to be equal to one and zero. Using this type of math, it would be easier to get infinity minus infinity to equal any real number. Therefore, infinity subtracted from infinity is undefined.
Answer and Explanation:
The largest real number is unknown and will never be known. This is because you can always get a larger number by adding one more to the number you have.
In modern mysticism, the infinity symbol has become identified with a variation of the ouroboros, an ancient image of a snake eating its own tail that has also come to symbolize the infinite, and the ouroboros is sometimes drawn in figure-eight form to reflect this identification—rather than in its more traditional ...
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.
Infinity is greater than any real number, so there is no “biggest” number. Whereas “finite” means we could eventually count to an end, infinite (or not finite) means never-ending and indefinite. Think about a line — it extends in both directions without end and contains an infinite number of points.
A thousand trillions is a quadrillion: 1,000,000,000,000,000. A thousand quadrillions is a quintillion: 1,000,000,000,000,000,000.
The concept of zero and that of infinity are linked, but, obviously, zero is not infinity.
Different infinite sets can have different cardinalities, and some are larger than others. Beyond the infinity known as ℵ0 (the cardinality of the natural numbers) there is ℵ1 (which is larger) … ℵ2 (which is larger still) … and, in fact, an infinite variety of different infinities.
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.
We can say that the division by the number 0 is undefined among the set of real numbers. $\therefore$ The result of 1 divided by 0 is undefined. Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number.
Infinity is bigger than any number. But saying just how much bigger is not so simple. In fact, infinity comes in infinitely many different sizes—a fact discovered by Georg Cantor in the late 1800s.
Is Pi bigger than infinity? Pi is finite, whereas its expression is infinite. Pi has a finite value between 3 and 4, precisely, more than 3.1, then 3.15 and so on. Hence, pi is a real number, but since it is irrational, its decimal representation is endless, so we call it infinite.
Person 1: “Noooo — it's infinity +1!” The thing is, infinity is not a number, but a concept or idea. A "googol" is the number 1 followed by 100 zeroes. The biggest number with a name is a "googolplex," which is the number 1 followed by a googol zeroes.
The answer depends on which notion of infinity we use. The infinity of limits has no size concept, and the formula would be false. The infinity of set theory does have a size concept and the formula would be kind of true. Technically, statement 2∞ > ∞ is neither true nor false.
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! A larger infinity can always be constructed.
Infinity is a mathematical concept originating from Zeno of Elia (~450 BC) who tried to show its “physical” impossibility. This resulted in the “arrow paradox”, but which was solved later on. Many mathematicians and physicists went on to try understanding infinity and to explain it by various theories and experiments.