No, infinity is not a number and cannot be compared to a finite value like googolplex.
Response to the query in detail
The answer to the question “Is googolplex higher than infinity?” is “No, infinity is not a number and cannot be compared to a finite value like googolplex.” This is because “infinity” refers to the concept of endlessness, not to a specific quantity. As the mathematician David Hilbert said, “The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea.”
Interesting facts about googolplex and infinity:
- A googol is 1 followed by 100 zeros, and a googolplex is 1 followed by a googol of zeros.
- A googolplex is such a large number that it is physically impossible to write it out in full, even if we used all the matter in the universe to make the digits.
- The number of atoms in the observable universe is estimated to be around 10^80, which is much smaller than a googol.
- Infinity is not a number in the traditional sense and cannot be expressed as a finite quantity.
- Infinity is used in mathematics to represent a concept of unboundedness, such as the limit of a sequence that grows without bound.
- There are different sizes of infinity in mathematics, the smallest of which is called aleph-null or countable infinity.
- Georg Cantor famously proved that some infinities are larger than others, showing that the set of real numbers is uncountably infinite.
Here is a table comparing the size of different numbers:
| Number | Digits | Size |
|---|---|---|
| 10 | 2 | Ten |
| 100 | 3 | One hundred |
| 1000 | 4 | One thousand |
| 10,000 | 5 | Ten thousand |
| 1M | 6 | One million |
| 1B | 9 | One billion |
| 1T | 12 | One trillion |
| 1Q | 15 | One quadrillion |
| 1P | 18 | One quintillion |
| 1E | 21 | One sextillion |
| 1Z | 24 | One septillion |
| 1Y | 27 | One octillion |
| Googol | 100 | Ten duotrigintillion |
| Infinity | N/A | Endless |
See the answer to your question in this video
The video explores the concept of infinity and the fact that some infinities are bigger than others. The first and smallest infinity is aleph null, which represents the number of natural numbers, even numbers, odd numbers and fractions. The speaker introduces the idea of ordinal numbers as a way of labeling collections in order, rather than cardinality. Ordinals reveal infinities larger than aleph null, such as the power set of aleph null, which contains many more members. Using diagonalization, it’s possible to create a new subset that will always be different in at least one way from every other subset and prove that there are more cardinals after aleph-null. The video explores the concept of inaccessible numbers which require the same axiomatic declaration for existence as aleph null but continue to grow in height as set theorists describe numbers bigger than inaccessibles.
Other viewpoints exist
Everyone loves to pull out infinity, or the fabled “infinity plus one.” Maybe if you were inclined to do so, you pulled out the googol or the googolplex. Smaller than infinity, but really big numbers each.
A googolplex is many, many times larger than a googol, which is the largest number named with a single word. It is impossible to write all the zeros out, as there would be ten-duotrigintillion of them. Counting to a googolplex would be even more impossible, and it is estimated that it would take longer than the age of the universe. However, infinity is not a number, and therefore cannot be compared to googolplex.
Googolplex may well designate the largest number named with a single word, but of course that doesn’t make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number… Child: Infinity! Nothing is larger than infinity!
As massive as a googol is, a googolplex is many, many times larger, such that it’s impossible to write all the zeros out. There’d be ten-duotrigintillion of them! Counting to a googolplex would be even more impossible. We can’t calculate how long it would take, but it’s estimated it would take longer than the age of the universe.
More interesting on the topic
Regarding this, Is a googolplex bigger than infinity? Googolplex may well designate the largest number named with a single word, but of course that doesn’t make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number… Child: Infinity! Nothing is larger than infinity!
Similar
What number is bigger than googolplex? Response to this: What’s bigger than a googolplex? Even though a googolplex is immense, Graham’s number and Skewes’ number are much larger. Named after mathematicians Ronald Graham and Stanley Skewes, both numbers are so large that they can’t be represented in the observable universe.
Just so, What is higher than infinity?
Infinity means limitless Therefore there is no number more than infinity It is just a description that means boundless and has no end. Helpful(1)
What is the biggest number below infinity?
There is no biggest, last number … except infinity. Except infinity isn’t a number.
In this way, What is a googolplex?
As an answer to this: At the same time that he suggested "googol" he gave a name for a still larger number: "googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired.
Is Graham’s number bigger than a googolplex?
See YouTube or wikipedia for the defination of Graham’s number. A Googol is defined as 10 100. A Googolplex is defined as 10 Googol. A Googolplexian is defined as 10 Googolplex. Intuitively, it seems to me that Graham’s number is larger (maybe because of it’s complex definition).
Also question is, Is googolplexian less than 3 6? So, Googolplexian is much smaller than a tower of exponents of 3 ‘s of length 6, or in other words Googolplexian is less than 3 ↑↑ 6. (using Knuth’s up-arrow notation .) Now, compare this with just the first layer of Graham’s number,i.e., 3 ↑↑↑↑ 3.
In this way, Can a googolplex be written in decimal form? Answer will be: In the PBS science program Cosmos: A Personal Voyage, Episode 9: "The Lives of the Stars", astronomer and television personality Carl Sagan estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000…") would be physically impossible, since doing so would require more space than is available in the known universe.
Correspondingly, Is googolplex greater than infinity?
Response will be: No. Googolplex is equal to 10^googol which is 1 followed by zeroes. Infinity is greater than all numbers. If we were to define it using exponents, it would be Which is greater? or ? Is a googolplexianthenialarisian bigger than Graham’s number? I have never heard of this number, but I will assume it is googolhexiplex (10^10^10^10^10^10^100)
Similarly, What is a googolplex? Response will be: At the same time that he suggested "googol" he gave a name for a still larger number: "googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired.
Considering this, What is the difference between googolplexian and googol?
Googolplexian is “ten to the power googolplex”, while googolplex is “ten to the power googol”, and googol is “ten to the power one hundred”. In other words, googol is 1 followed by a hundred zeroes, googolplex is 1 followed by a googol zeroes, and googolplexian is 1 followed by a googolplex of zeroes.
One may also ask, Is Graham’s number bigger than a googolplex?
See YouTube or wikipedia for the defination of Graham’s number. A Googol is defined as 10 100. A Googolplex is defined as 10 Googol. A Googolplexian is defined as 10 Googolplex. Intuitively, it seems to me that Graham’s number is larger (maybe because of it’s complex definition).