## The Largest Number We Will Ever Need

• 4.7k
I would like to re-address the issue of the OP, expressed in the title:
(What is the) The Largest Number We Will Ever Need (?)
I'd say one, if all other axioms in the mainstream system are applied. 1. It can be added, the sums can be multiplied or divided or subtracted from each other, and the whole shkebam can be developed just form one number, which is one.

This is a specific example of the largest number. It could be a half, a million, any number, really, real or imaginary, and rational or irrational. Any one number could satisfy the question, "What is the largest number we shall ever need?" Provided, of course, that the generation of other values, expressed in numbers, in an infinite variety, is possible from the axioms used.
• 7.6k

That's wonderful. :up:

All we need to get the ball rolling is 1.

Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved. — Charles Darwin

Le Monad.
• 692
Which means ∞∞ is impossible, squaring with Aristotle's decision to make the distinction potential vs. actual (infinity).

Can infinity even be considered as possible or impossible? it's a concept. If an axiom calls it to be true/in need then I see no reason to assume otherwise.
• 7.6k
Can infinity even be considered as possible or impossible? it's a concept. If an axiom calls it to be true/in need then I see no reason to assume otherwise.

I haven't read the original argument made by Aristotle - Wikipedia offers only a rough sketch. It seems as though Aristotle considered real/actual entities as those that had an end; consider the process of constructing a chair. It begins (wood, nails, glue, etc.) and ends (a chair). If one is unable to complete the task, we have a potential chair and not an actual one. The same goes for $\infty$, it, by definition is endless.
• 4.7k
I haven't read the original argument made by Aristotle - Wikipedia offers only a rough sketch. It seems as though Aristotle considered real/actual entities as those that had an end; consider the process of constructing a chair. It begins (wood, nails, glue, etc.) and ends (a chair). If one is unable to complete the task, we have a potential chair and not an actual one. The same goes for ∞∞, it, by definition is endless.

I don't agree that it's a valid application of Aristotle's rule of the difference between actual and potential.

The infinity is there. The only reason it can't be counted is because counting is a process which is always finite. However, it is the tool of the test, the counting, that is the culprit here, so to speak; it is the weakness of the tool that stops us from realizing the actuality of infinity.

If there were an instrument that meausred infinity, then the actuality would immediately show through.
• 692

If there were an instrument that meausred infinity, then the actuality would immediately show through.

I think this is a good point. It would be harmful to assume that infinities don't exist in the real world simply because we can't process them in a tangible manner.
• 7.6k

Yeah, we need a different tool!
• 692
d; consider the process of constructing a chair. It begins (wood, nails, glue, etc.) and ends (a chair). If one is unable to complete the task, we have a potential chair and not an actual one.

What about a cyclical process?
• 7.6k
What about a cyclical process?

I proposed that; no takers!
• 692

Why? First Cause?
• 692
If, a big if, there did exist a finite number Nmax that could stand in for, salva veritate, ∞∞, we could prove/disprove all mathematical conjectures via proof by exhaustion (brute search) with the help of existing supercomputers

Some mathematical systems require an infinite set to function. I think it's just a question of where your looking at; assuming infinity isn't intrinsically false, or bad, it's just another way to look at something, which happens to have some pretty interesting conclusions.
• 692
Here's a page I found that I think is relevant to the topic:

https://en.wikipedia.org/wiki/Axiom_of_choice
• 7.6k
Why? First Cause?

Dunno!
• 99
"Will this post have good outcomes, will it be productive, is it free of any breach of virtue that will harm my character?" and it would be nuts for me or anyone to expect they would.

I will say that the benefit of virtue ethics is that you'll no longer have to reconsider this in straightforward situations that are not ethical dilemmas. In acting virtuously, virtuous action becomes habit
• 1.7k
"Will this post have good outcomes, will it be productive, is it free of any breach of virtue that will harm my character?" and it would be nuts for me or anyone to expect they would.

That makes it appear that I said that we can't expect that posts have good outcomes, etc.

But what I posted:

Posters don't ordinarily think "Will this post have good outcomes, will it be productive, is it free of any breach of virtue that will harm my character?" and it would be nuts for me or anyone to expect they would.

That is to say that I don't expect that ordinarily posters ask those questions before posting.

In acting virtuously, virtuous action becomes habitKuro

I understand that view.
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