How To Count Past Infinity

TL;DR

The biggest number is 40 in terms of surface area, but in terms of the amount of things, there is no biggest last number except infinity, which is a kind of number that requires infinite numbers to talk about and compare amounts. This video delves into the concept of infinity, including aleph null, ordinal numbers, and the existence of inaccessible cardinals.

Transcript

hey vsauce michael here what is the biggest number you can think of a google a google plex a millimillion olplex well in reality the biggest number is 40. covering more than 12 000 square meters of earth this 40 made out of strategically planted trees in russia is larger than the battalion markers on signal hill in calgary the six found on the fove... Read More

Key Insights

• 😃 The biggest number in terms of surface area on earth is 40, representing a strategically planted tree formation in Russia.
• #️⃣ There is no biggest last number when it comes to the amount of things, except for infinity, which requires infinite numbers to compare unending amounts.
• #️⃣ Aleph null is the first smallest infinity and represents the number of natural numbers, even numbers, odd numbers, and fractions.
• 😫 Ordinal numbers describe the arrangement and order type of sets, including omega as the first transfinite ordinal.
• 😫 The power set of a set contains more members than the original set, with the number of members being two to the power of the original set's size.
• 😃 Replacement and repeated power sets allow us to reach larger and bigger infinities from aleph null.
• 👶 Inaccessible cardinals represent numbers unreachable from below and require the introduction of new axioms to assert their existence.

Questions & Answers

Q: What is the biggest number in terms of surface area on the earth?

The biggest number in terms of surface area on earth is 40, which represents a strategically planted tree formation in Russia covering over 12,000 square meters.

Q: Is there a biggest last number when it comes to the amount of things?

No, there is no biggest last number when it comes to the amount of things except for infinity. Infinity is not a number but a concept that requires infinite numbers to compare and talk about unending amounts.

Q: What is aleph null?

Aleph null is a concept that represents the number of natural numbers, including even numbers, odd numbers, and fractions. It is the first smallest infinity and is used as the cardinality for counting how many things there are.

Q: What are ordinal numbers?

Ordinal numbers describe the arrangement of sets and the order in which elements appear. They provide the order type of a set and can be used to label elements based on their position. Omega is the first trans-finite ordinal, with omega plus one, omega plus two, and so on representing different arrangements.

Q: Can we count past aleph null?

Yes, we can count past aleph null by using supertasks and creating infinite sequences. However, the quantity of things remains the same, as we can always match the naturals one-to-one with the added lines or sequences.

Q: What is the power set of a set?

The power set of a set is the set of all possible subsets that can be formed from the original set. It contains more members than the original set, with the number of members being two to the power of the original set's size.

Q: Can we reach larger infinities from aleph null?

Yes, by using replacement and repeated power sets, we can reach larger infinities from aleph null. We can make jumps of any size using replacement and create sets with even bigger numbers.

Q: What are inaccessible cardinals?

Inaccessible cardinals are numbers so big that they cannot be reached from below using replacement and power sets. They require the declaration of a new axiom to assert their existence and represent a conceptual jump to even larger infinities.

Summary & Key Takeaways

• The biggest number on earth is 40, which covers more than 12,000 square meters of land in Russia.

• 40 is the biggest number in terms of surface area, but when it comes to the amount of things, there is no biggest last number except infinity.

• There are different types of infinity, such as aleph null, which represents the number of natural numbers, and ordinal numbers, which describe the arrangement of infinite sets. The existence of inaccessible cardinals suggests numbers even bigger than previously imagined.