# Theory of Infinity: Exploring Boundless Possibilities

• cubed
In summary, the conversation discusses the concept of infinitesimal numbers and their use in calculus and other fields of mathematics. While some argue that infinitesimals have intuitive appeal and can lead to shorter and cleaner proofs, others argue that they are not true numbers and should not be treated as such. The conversation also touches on the idea of infidentiality, which is not related to mathematics but rather a humorous play on words.
cubed
This is the theory I made, saying that every moment is infidential.
Lets just say 1 second can be dividied into 100milliseconds, and 100milliseconds can be divided into the next smallest unit and so, this process is infidential...
Same with digits.
Lets take an interger 1. We can divide it into smaller units.(decimals)
lets divide them into 0.111, and let's compare it to 0.1111 it's not the same eg, 0.1 is equal to 0.10000. But digits are made of infinity.
0.4124685454, it can have as much division but it can be divided into units of infinity...

Haha, many people have stated something similar over and over again and often by doing this they get very confused and lost on where the actual maths is.

The only infinitesimal number (a number infinitely small) in the real numbers is 0.

There are other types of numbers though where you do get infinitesimal numbers other than 0 and if you are interested I'm sure one of our members can find a link on such numbers, they are a interesting read often.

yeah so doesn the mean that because o is smaller than the reciprocal of infinity
that the reciprocal of 0 is greater than infinity

That is true and you run down the battery to your calculator what is the point.

A definition of "infinitessimal" that is usually right is this:

A number x is infinitessimal if and only if |x| < 1 / n for every positive integer n.

Yes it is correct but what is the point. It is used slightly in differential and integral calculus and in geometry (forget the application). I remember it dealt with rotation. It might be slightly useful for Planck's length.

No one has pointed out an application.

Knowledge is only usefull if applied.

The "infintiessimals" you see in standard analysis are in quotes: they're not the real deal.

Recall that Newton's invention of calculus was based on infinitessimals -- the derivative was an infinitessimal quantity divided by another infinitessimal quantity, which happily gave a finite quantity we could manipulate.

Clearly, infinitessimals have some intuitive appeal. And if Mathworld is to believed, infinitessimal based approaches to analytic theorems tend to be, on average, shorter and cleaner than standard proofs.

Try looking into Nonstandard Analysis.

Hurkyl, just a note:
Newton is quite explicit on that the numerator and denominator should NOT be considered as numbers on their own; it is their limiting fraction which is a well-defined number.
He makes a great analogy by saying that if we looked at an expression like $$\frac{2x}{x}$$ and then made x as big as we wanted, then no one would say that either the numerator or denominater qualified as numbers, yet the fraction is well-defined in the limit..
In his theory of fluxions, it is the quantity $$\frac{\dot{y}}{\dot{x}}$$ he ascribes meaning, the fluxions themselves are seen as little more than convenient tools for calculation with not much meaning by themselves.

It was Leibniz who thought of infinitesemals as numbers, not Newton.

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You are all wrong.

In his post he does not use the word infinitesimal. He uses the word infidential. Infidential means "to dentistrify", where dentistrify means "to perform dentistry upon oneself." With a little context it is clear that the OP is a tale of masturbatory orthodonty, during which one's teeth are cleaned with a very, very thin floss.

## What is the theory of infinity?

The theory of infinity is a mathematical concept that deals with the concept of endlessness or boundlessness. It explores the idea that there are infinite quantities, sizes, and possibilities in the universe.

## How is the theory of infinity relevant in science?

The theory of infinity has many applications in science, particularly in fields like physics and cosmology. It helps us understand the vastness and complexity of the universe, and how it may be infinite in size and scope.

## What are some real-life examples of infinity?

Some real-life examples of infinity include the endlessness of numbers (there is always a number larger than any given number), the infinite nature of the universe, and the concept of time (which may be infinite and never-ending).

## What are the different types of infinity?

There are many different types of infinity, including countable and uncountable infinity. Countable infinity refers to sets that have an infinite number of elements, but can still be counted (e.g. the set of natural numbers). Uncountable infinity refers to sets that have an infinite number of elements that cannot be counted (e.g. the set of real numbers).

## What are some implications of the theory of infinity?

The theory of infinity has many implications for our understanding of the universe and our place in it. It challenges our traditional notions of limitations and boundaries, and opens up possibilities for infinite growth and exploration. It also raises philosophical questions about the nature of infinity and our ability to comprehend it.

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