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12 Examples of Infinity

Infinity is a concept that denotes something that has no end. Aristotle famously defined this as "'that which always has something beyond itself." As infinity can't be directly observed or measured in any traditional way, it is a fully abstract concept. People alternatively see it as intuitive and obvious or incomprehensible and frightening. The following are illustrative examples of infinity.

Potential Infinity

Potential infinity is infinity that can exist. This doesn't require that it actually exists such that it is easy to think of examples such as standard numbers that have no limit such that you can always make them larger from 1,2,3 ... ∞.


Potential infinity exists where anything is not given a limit. For example, computer code that contains a loop with no exit condition has potential to loop forever but this would require that the computer, electricity supply, human civilization and universe last forever.

Plato's Infinites

Plato believed that there are two infinities: small and large. For example, any line can be measured using increasing small points such that it contains infinite points. An example of infinitely large would be a line that goes off in a direction without ending.

Actual Infinity

Actual infinity is infinity that does exist or can truly exist in our universe. Examples of actual infinity can be designed in theory but it is often unknown if these can truly exist as they may create paradoxes or rely on unknowns. For example, numbers have potential to grow infinitely large but you wouldn't have time to count to infinity unless time itself is infinite.


Time is the ordering of events in a chain of cause and effect that appears to be a fundamental dimension of the universe. Intuitively people feel that time is infinite because it is difficult to imagine a universe without time. Various theories of time dispute this notion such as the theory of unreal time that states that time is simply a human perception that doesn't exist from the perspective of the universe itself.


It is unknown if the universe is infinite. People tend to feel intuitively that it is infinite because its hard to imagine the vast emptiness of space ending at a nothingness beyond which space doesn't exist. However, it is possible that space takes some form that is finite such as looping back into itself. As far as we can currently observe, space is enormous and unending.

Big Bang

When people speak of the universe they are typically referring to the observable universe that appears to be an explosion of matter and energy that occurred at a point of time and is still rapidly expanding. It is possible to estimate the size and age of the observable universe such that it isn't infinite. However, this is defined by how much we can observe. The big bang could be some tiny spec in a much larger or infinite universe.

Ultimate Fate of the Universe

The ultimate fate of the universe is the question as to the future of the big bang. This depends on several unknown factors, particularly the geometry of space. One prominent possibility known as the big freeze is that the universe continues to expand forever with this rate of expansion accelerating. According to this model, all matter and energy will be torn apart into smaller and smaller particles until the remaining particles are massless, cold and moving at the speed of light. This is an infinite process assuming that space is also infinite.


If space and time are infinite, this creates a bunch of actual infinities. For example, light traveling through space would travel forever as long as it didn't hit any matter that absorbed its energy.


A singularity is a change that occurs instantaneously and without limit such that it is essentially infinite. For example, the hypothesis that the density of a black hole at its center is infinite and that this state can occur in an instant.

Time Loop

Infinities often create paradoxes or are created by paradoxes. For example, the grandfather paradox whereby you invent a time machine and go back in time to disrupt your own birth. This can result in an infinite time loop as follows.
The solution above assumes that going back in time doesn't create another instance of the universe as would be predicted by multiple universe theory.

Zeno's Paradox

Zeno's paradox is a simple thought experiment:
An architect finishes half the remaining work on a building each day. When will the building be complete?
Many people find the answer to Zeno's paradox to be non-intuitive. By completing half the remaining work each day, the architect keeps making the remaining work smaller and smaller towards infinity but never completes. This can be seen on real projects that are impossible or infeasible to complete where progress is continually reported but the end date of the project will never come. Such a project may quickly reach 99% completion but will never reach 100%.
Overview: Infinity
Definition (1)
Something that has no limit.
Definition (2)
That which always has something beyond itself.
Related Concepts


This is the complete list of articles we have written about paradox.
Abilene Paradox
Catch 22
Fermi Paradox
Grandfather Paradox
Jevons Paradox
Paradox Of Choice
Password Paradox
Rational Thought
Thought Experiment
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The definition of paradox with examples.

Paradox Of Choice

The definition of paradox of choice with examples.

Tolerance Paradox

An overview of tolerance of intolerance.

Grandfather Paradox

The common solutions to the grandfather paradox.


A list of interesting contradictions.


An overview of philosophy with examples.


The definition of altruism with examples and counterexamples.


A list of virtues including the twelve virtues of Aristotle.

Nietzsches Philosophy

A summary of the philosophy of Friedrich Nietzsche.

Socrates Philosophy

A summary of the philosophy of Socrates.


The definition of alienation with examples.

Human Nature

A list of the common elements of human nature.

Plato Philosophy

An overview of the important theories of Plato.


The definition of rationalism with examples.
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