Arguments for the existence of infinity

What is the argument of infinity?

According to the Infinity Argument, an actually infinite regress of past events cannot exist because an actual infinite cannot exist. The Infinity Argument is one of the most common arguments for a beginning of the universe espoused by advocates of the kalām cosmological argument.

Can an actual infinity exist?

In the context of a number system, in which “infinity” would mean something one can treat like a number. In this context, infinity does not exist.

Why actual infinity is impossible?

According to Aristotle, actual infinities cannot exist because they are paradoxical. It is impossible to say that you can always “take another step” or “add another member” in a completed set with a beginning and end, unlike a potential infinite.

How can you prove infinity?

When I was taught mathematics infinity was considered as provable as 1 + 1 = 2, and it was proven to us by our teachers using the fact that given any number, it was always possible to create a new number by adding one. But confusingly there is no proof that infinity exists.

What does infinite mean philosophy?

Aristotle and after

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It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number.

What does Aristotle say about infinity?

Aristotle postulated that an actual infinity was impossible, because if it were possible, then something would have attained infinite magnitude, and would be “bigger than the heavens.” However, he said, mathematics relating to infinity was not deprived of its applicability by this impossibility, because mathematicians …

Is infinity a paradox?

The paradox states that you can still fit another infinite number of guests in the hotel because of the infinite number of rooms. If the rooms were full, then there is a last room, which means that the number of rooms is countable. To solve this paradox, we must first make it clear that infinity is not a number.

Is infinite truly infinite?

The universe could be infinite, both in terms of space and time, but there is currently no way to test whether it goes on forever or is just very big. The part of the universe we are able to observe is finite, measuring about 46 billion light years in diameter.

Is infinity a fact?

Some infinities are bigger than others. The smallest infinity is how many whole numbers there are: 1, 2, 3, 4 and so on forever. If we include fractions there are infinitely many more numbers. In fact there are infinitely many fractions in between each whole number.

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Is infinity infinity defined?

There is no answer to this. Since, infinity is not really a number, we cannot treat it in the same manner we treat “numbers” i.e we cannot perform mathematical calculations on Infinity. Due, to the above, what “minus” exactly means for infinity isn’t clear.

What’s the biggest infinity?

There is no biggest, last number … except infinity. Except infinity isn’t a number. But some infinities are literally bigger than others.

Is infinity plus 1 still infinity?

Asked by: Nick Cooper, Bristol

Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.

What’s the value of infinity?

The initial value of Infinity is Number.

What’s better than infinity and beyond?

Different infinite sets can have different cardinalities, and some are larger than others. Beyond the infinity known as ℵ (the cardinality of the natural numbers) there is 1 (which is larger) … 2 (which is larger still) … and, in fact, an infinite variety of different infinities.

Does infinite have a beginning?

∞ has no end and no beginning: It is the end and the beginning.