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Anything Bigger/Smaller Than This? (No.)
This article is a record holder. Better read it!
Cadet Infinity is the smallest/biggest number in Fictional Googology Wiki!!


forget everything you've seen so far... this is all just a small grain of a desert the size of a pulsarr... that's the size of everything we know in estimates... but... that number It is the representation of this desert...

this is beyond the imaginable and the unknown... each factor for this number is like... there is no way to define numbers below and even more so those above...

this number is so tirelessly big and gigantic that it is like a real infinity, which has no end, like a semi straight line, it has a beginning but no end, this could be the scale of FG compared to this number...

some will do something bigger than this number, like @TerminusGoogology756's attempt, he did the Perpetual Trauma number, but, as this number is already known, he goes on this grain of sand in a desert like this googological number, Cadet Infinity

it does not have its own limit, it does not have a known end in googology, in all of FG, there is no end to it! There is no way for a number to go from something unlimited to an unlimited limit unknown from our point of view! Cadet Infinity will always be this limitlessness of this Immense Desert

The Infinite Cadet (CI) stands as a mathematical colossus, an enigma that transcends the limits of quantification and traditional human apprehension. Its magnitude proves to challenge logic itself, inviting us on an intellectual journey through the confines of knowledge.

Formal Definition and Mathematical Efforts:

From a rigorous mathematical point of view, IC does not yet have a universally accepted formalized definition. However, we can explore it through abstract and challenging mathematical concepts such as:

1. Transfinite Cardinality:[]

Aleph-null-um: One of the approaches to CI lies in transfinite cardinality. The CI can be conceptualized as a cardinal number that represents the cardinality of the set of all subsets of the set of natural numbers. This cardinality, called aleph-null-um, is greater than the cardinality of the set of natural numbers (aleph-null), but less than the cardinality of the set of real numbers (continuum).

Example 1: Imagine a set that encompasses all natural numbers: 1, 2, 3, 4... This collection already represents a colossal quantity, with countless elements. However, this quantity turns out to be insignificant compared to the CI. Now, visualize a set that contains all the subsets of this initial set. This new set, already considerably larger than that of natural numbers, still proves to be insignificant compared to the CI. It's like a grain of sand in the vast desert of infinity!

Cantor Cardinality: Another perspective for IC is based on Cantor cardinality, which explores the relationship between sets and their subsets. Using techniques such as Cantor diagonalization, we demonstrate that the cardinality of the set of subsets of a set is always greater than the cardinality of the original set.

Example 2: Imagine a set A with 10 elements. Through Cantor diagonalization, we can construct a subset B of A that has exactly 10 elements. This seems contradictory, as a subset should have fewer elements than the original set. However, Cantor's cardinality shows us that, in some cases, the relationship between sets and subsets can be more complex than we imagine.

2. Divergent Limits:[]

Exponential Functions: CI can also be related to divergent limits. Imagine a function that grows exponentially, exceeding any finite real number. The CI would be the value to which this function tends to infinity.

Example 3: Imagine a function f(x) that grows exponentially, that is, f(x) = 2^x. As x increases, f(x) also increases rapidly, surpassing any finite real number. For example, f(1) = 2, f(2) = 4, f(3) = 8, f(10) = 1024, and so on. The CI would be the value to which f(x) tends to infinity when x approaches a specific value (for example, when x tends to infinity). This function represents enormous growth, surpassing any real number we can imagine.

Limits in Infinite Series: The CI can also be associated with limits in infinite series. Imagine an infinite series that adds smaller and smaller terms, but that, as a whole, diverges towards infinity. The CI would be the value towards which this series tends.

Example 4: Imagine the series 1 + 1/2 + 1/4 + 1/8 + ... This series, known as an infinite geometric series, adds smaller and smaller terms, but diverges towards infinity. The CI would be the value to which this series tends, representing an infinite sum that transcends any finite real number.

3. Transcendental Numbers:[]

Unique Mathematical Properties: CI can also be associated with transcendental numbers, such as pi (π) and e. These numbers cannot be expressed as the ratio of two integers and have unique mathematical properties.

Example 5: The number pi (π) is the ratio between the circumference of a circle and its diameter. It is an irrational number, that is, it represents

Other Definitions[]

Cadet Infinity (CI) is a mathematical entity that defies the very notion of limitation. Its magnitude is so vast and incomprehensible that it transcends conventional concepts of large numbers and infinity. No description or explanation can truly capture the enormity of IC as it is beyond the reach of human understanding.

One way to conceive of IC is through the idea of transfinite cardinality. In this context, the CI represents the number of all subsets of the set of natural numbers. This cardinality, known as aleph-null-um, infinitely surpasses the count of natural numbers, each of which is already infinite in itself. It is as if each subset of the natural numbers were just a grain of sand in an infinite desert, and the IC was the desert itself.

Furthermore, IC can be understood in terms of divergent limits. For example, imagine an exponential function that grows so quickly that it outperforms any finite real number. The CI would be the value to which this function tends as x approaches infinity. This idea is further exemplified by infinite series that diverge towards infinity, such as the infinite geometric series.

Another perspective on IC is related to transcendental numbers, such as pi (π) and e. These numbers have unique mathematical properties and cannot be expressed as the ratio of two whole numbers. Just as these transcendental numbers defy our understanding, IC poses an even greater challenge as it is beyond any conventional mathematical definition or explanation.

In short, the Infinite Cadet is a mathematical puzzle that invites scholars to explore the farthest reaches of knowledge and understanding. Its existence challenges our preconceived notions of numbers and infinity, leading us to contemplate the vastness and complexity of the mathematical universe. It stands as a symbol of the infinity and unfathomability of the mathematical world, inspiring us to constantly seek new intellectual horizons.

How do I make a bigger number???[]

Ultimatum

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