Infinity Misconception – Understanding the Concept

Infinitesimal & Infinite – Elementary Considerations

Probably the most misunderstood aspect when considering the concept of infinity, is what infinity is supposed to be/mean?

Infinity is neither an extremely large size, nor indeed an extremely small size, both of which are simply finite numerical values.

There is only one true! logical definition (meaning) of infinity, as identified in this website's definitions category – infinity is not a number!

It’s an idea that attempts to have us believe the impossible – after adding or subtracting any quantity, infinity's supposed quantitative-like existence remains unchanged, i.e., infinity cannot shrink or grow in size – infinity never exists as a specific size.

Misunderstood Term “Potential-infinity”

Potential-infinity is a misnomer! Any numerical value which increases or decreases indefinitely is simply changing to become another value – any changing numerical value will always remain a finite size, i.e., an actual value – which is no surprise of course.

The term “infinity” might well be convenient for referring to indefinitely changing values, but it comes at a price – a misconception. People are even being taught that infinities of different sizes actually exist... bonkers!

By using “infinity” it makes it easy to express the significance of indefinitely changing values, but the true logical meaning of infinity is all about pre-existing infinite state – set theory incorrectly assumes the platonical existence of numbers – calculus and asymptotic relationships are sometimes mistakenly believed to represent infinite states of existence.

Incoherent Terminology Example

This example applies to dictionary definitions of infinity: 1, 2, and 4, as quoted in this website's definitions.

The total amount of space in the universe is infinite.” – the word “total” means all of (entire) something, and a supposed infinite amount of anything cannot be encapsulated, i.e., if there’s no boundary, there’s no numerical size; space wouldn’t even have a shape! – it would be shapeless, i.e., not even spherical as might seem intuitive to imagine.

Infinity via Extra Spatial Dimensions

  1. Are extra dimensions excused from logical numerical analysis? The answer is no – therefore there cannot exist an infinite number of extra dimensions because it is impossible for an infinite physical state (or indeed theoretical state) of anything to exist – the simple counting paradox, i.e., impossible to count means not part of a totality and therefore cannot exist.

  2. It is impossible for a mathematical expression to equal infinity. Sure, things can be written down such as 1/3 = 0.33333 ... but those three dots (“...”) != infinity. Likewise, the axiom of infinity is no more meaningful. Such things are simply declarations; like saying there actually exists some pre-existing infinite state simply because we say so.

  3. Models of multidimensional space that are asserted to be infinite in their capacity in order for them to contain an infinite number of physical realities are in error – the only mathematical expression that can even attempt to equal infinity is... any finite value divided by zero... such as 1/0 which is undefined, i.e., nonsensical; no result can be written down, calculated, or computed.

Typically, imagination has a hard time trying to process the perplexing nature of the idea of infinity, and an even harder time trying to process existence without infinity – even some of the most academically gifted mathematicians and scientists seem to accept the idea, without even questioning its validity.

Infinity via Three-Dimensional Space

  1. Can the divisibility of space and time really have a meaningful existence in the reality we experience, if the Planck units of space and time exist as being divided incomprehensibly smaller, i.e., to the point that they don’t even exist via a numerical value?

  2. If divisions of space and time exist somewhere above 0 in value, but below any possible numerical value, what does that even mean? How is that a quantitative existence in any sense? And if it isn’t a quantitative existence, why is it sometimes accepted as not representing an error within mathematics?

Answer to all the above: Infinity is a misconception!

Infinity in a Nutshell

  1. Things cannot actually exist without being part of a totality. For things that do actually exist, the words “All" and “Whole" can indeed be used to refer to their “Total” quantity of existence.

  2. Infinitely small is used to attempt to refer to infinitely many numerical values within a given finite numerical value.

  3. Infinitely large is used to attempt to refer to values which are beyond any possible finite value.

  4. No addition of values each above 0 can fit into any finite size an infinite number of times, therefore things cannot be infinitely divisible.

  5. No position (location) in straight-line space can exist without being connected to every other position via relative coordinates – supposed infinitely faraway locations cannot possibly be connected to our location, therefore they don’t exist.