Multiplying 0 by infinity is the equivalent of 0/0 which is undefined.
Zero multiplied by infinity will be Zero itself. However the answer should depend on weather it is exact zero or tending zero. When zero is multiplied by x where x tends to infinity, the answer will be zero. And when Y is multiplied by X where Y tends to zero and X tends to infinity, answer will be Indeterminate.
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 same holds true for limits so if you have an even number of limits, you get a real number, or in this equation, 1.
Rebuttal: But any number multiplied with zero is zero, why is this not the case here? Reply: You are correct, but infinity is not a number. And hence it does not apply to infinity.
Multiplication Property
If a number is multiplied by infinity, then the value of the product is also equal to infinity.
This value behaves mathematically like infinity; for example, anything multiplied by Infinity is Infinity, and anything divided by Infinity is 0.
What we'll focus on in this lesson is giving precise meaning to the phrase “infinity times 2 is infinity”. Actually, what we'll show, is that “infinity type 1 times 2 is infinity type 1”. and so on.
The concept of infinity varies accordingly. 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.
If you're thinking of infinity as a number, then zero times infinity is not defined. You'll often find it given as NaN, "not a number", on a computer. If you're thinking of it as a form of a limit, it's an indeterminate form, and the limit may or may not exist.
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.
If you want to count to infinity by enumeration: 1,2,3,..., you will never be able to reach infinity, no matter how fast you will count.
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. In the case of limits, we only assume that the value of limit x tends to something and not equal to something. So, we consider it infinity.
Multiplying infinity by infinity will result in infinity.
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 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.
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.
Potential infinity is never complete: elements can be always added, but never infinitely many. "For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different." — Aristotle, Physics, book 3, chapter 6.
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.
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.
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.
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.
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.
What is the world's biggest number? There is no biggest number, you cannot run out of numbers. We will never run out of numbers, even if going beyond a certain point removes any semblance of importance and real-world application. There is no end in sight for numbers, but we will have to come up with new names for them.
∞ is not a real number and you cannot multiply with it. What I would say is that you can multiply any non-zero number by infinity and get either infinity or negative infinity as long as it isn't used in any mathematical proof. Because multiplying by infinity is the equivalent of dividing by 0.