No, googolplex is not greater than infinity.
Explanatory question
No, googolplex is not greater than infinity. In fact, infinity is not a number that can be exceeded or surpassed by any finite number, no matter how large.
According to physicist and cosmologist Neil deGrasse Tyson, “Infinity is not a number, it’s a concept.” This means that infinity cannot be quantified in the same way that numbers can be. Therefore, any comparison between infinity and a number, including googolplex, is not valid.
However, it is still interesting to note some facts about googolplex. A googolplex is defined as 10 to the power of a googol, which is 10 to the power of 100. To put this into perspective, the number of particles in the observable universe is estimated to be within the range of 10^78 to 10^82. This means that a googolplex is an incredibly large number that is beyond human comprehension.
To further illustrate the vastness of a googolplex, consider this: if you were to write out every digit of a googolplex in standard form, using a font size of 10 point, it would stretch for over 13 billion light years, which is larger than the observable universe. It is clear that even though googolplex is an enormous number, it is still incomparable to infinity.
Table:
| Googol | Googolplex |
|——–|————|
| 10^100 | 10^(10^100)|
Video answer to your question
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 answers to your question
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.
No, a googolplex is not smaller than infinity. A googolplex is a very large number, equal to 10 to the power of a googol (10^(10^100)), but it is still finite. Infinity, on the other hand, is not a finite number and therefore is not comparable to a googolplex.
No, a googolplex is not smaller than infinity. A googolplex is a very large number, equal to 10 to the power of a googol (10^(10^100)), but it is still finite. Infinity, on the other hand, is not a finite number and therefore is not comparable to a googolplex.
It is true that the word “googolplex” was coined to mean a one followed by a googol zeros. True enough, but there is nothing as large as infinity either: infinity is not a number.
Surely you will be interested in this
Is googolplex higher 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!
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Keeping this in view, What is higher than a googolplex? 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.
What is bigger than infinity?
Response to this: 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.
Accordingly, Which is larger infinity or googol? The response is: 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.
Beside above, Is infinity a googolplex? Nope. A googolplex is a number, a very big number, but one that is fixed in size. Infinity is more of a concept than a number. Infinity doesn’t have an end, it keeps on going. Which is bigger, a Googolplexianth or Graham’s number?
Moreover, What is a googolplex?
A googolplex is 10^10^100, where the exponents are solved from the right. The exponentiation symbol (^) means the number just to the left multiplied by the left number’s self the number just to the right number of times. If the left number is 10, that means 1 followed by the right number of zeros.
What is the difference between googolplexian and googol? The reply will be: 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.
Furthermore, Is Graham’s number bigger than a googolplex?
Answer will be: 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 Know, Is infinity a googolplex? Nope. A googolplex is a number, a very big number, but one that is fixed in size. Infinity is more of a concept than a number. Infinity doesn’t have an end, it keeps on going. Which is bigger, a Googolplexianth or Graham’s number?
Consequently, 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.
Hereof, Is Graham’s number bigger than a googolplex? The reply will be: 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).
Similarly, How big is a googolplex?
A googolplex is without a doubt incredibly large, it’s 10^10^100 or 10^googol which is a one followed by a googol zeroes, a googol is already a larger number than the number of atoms they’re are in the observable universe, so you need more space than there is in the observable universe just to write a googolplex in its full digital form.