What is 0 into infinity?
If zero is divided by infinity, the result is 0.
Answer and Explanation: We cannot really divide infinity by zero because infinity is not a number and we do not divide by zero. However, we can use limits to determine what happens when we divide an extremely large quantity (almost infinitely large) by an extremely small quantity (very close to a zero).
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 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.
And so on. Regardless of what large number we're dividing by our answer is 0 and by letting this large number increase (as much as we please, tending to infinity) the answer is still 0. Thus the 'answer' to your question is 0.
Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity, ie: Suppose you set x=0/0 and then multiply both sides by 0. Then (0 x)=0 is true for most any x-- indeterminant.
As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0.
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.
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.
The number 0 is the smallest non-negative integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number (as well as an algebraic number and a complex number).
Is infinity plus 1 bigger than 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.
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.
| Name | The Number | Symbol |
|---|---|---|
| quintillion | 1,000,000,000,000,000,000 | E |
| quadrillion | 1,000,000,000,000,000 | P |
| Very Small ! | ||
| quadrillionth | 0.000 000 000 000 001 | f |
There is no biggest, last number … except infinity. Except infinity isn't a number. But some infinities are literally bigger than others.
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.
Hence, 5 divided by infinity is 0. Alternatively, we know that any number divided by 5 is equal to 0. Therefore, 5 divided by 0 is 0.
As we cannot guess the exact number, we consider it as a length of a number or infinity. In normal cases, the value of something divided by 0 has not been set yet, so it's undefined.
Just say that it equals "undefined." In summary with all of this, we can say that zero over 1 equals zero. We can say that zero over zero equals "undefined." And of course, last but not least, that we're a lot of times faced with, is 1 divided by zero, which is still 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. 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.
So the only boundary point of [0,∞) and (0,∞) is 0 itself. It is in [0,∞), so that set is closed. It is not in (0,∞), so that set is open.
Why is 0 * infinity undefined?
First of all, infinity is not a real number so actually dividing something by zero is undefined. In calculus ∞ is an informal notion of something "larger than any finite number", but it's not a well-defined number.
The sequence of natural numbers never ends, and is infinite. OK, 1/3 is a finite number (it is not infinite). There's no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like "0.999..." (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s.
Just say that it equals "undefined." In summary with all of this, we can say that zero over 1 equals zero. We can say that zero over zero equals "undefined." And of course, last but not least, that we're a lot of times faced with, is 1 divided by zero, which is still undefined.
−1∞ is 0. Any value divided by infinity is 0 except infinity divided by infinity, which is undefined.
This question already has answers here:
Closed 8 years ago. Any number multiplied by 0 is 0. Any number multiply by infinity is infinity or indeterminate.
This is known to be a bijection from R→(0,∞). Therefore, R and (0,∞) have the same cardinality.
Therefore, infinity divided by infinity is NOT equal to one. Instead, we can get any real number to equal to one when we assume infinity divided by infinity is equal to one, so infinity divided by infinity is undefined.
Infinite exponentiation means that you take 1 and multiply it by a scaler, a, infitnite number of times. Scaling by a > 1 yields greater and greater number. So, (a>1)∞=∞.
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.
Also, in some calculators such as the TI-Nspire, 1 divided by infinity can be evaluated as 0.