Infinity is not a quantity: infinity is a concept: as the infinity of skirts(if this be actual) would not be a skirt. In Logic infinity is defined presupposing a concept(i.e. of a set) as the cardinality of this set, in order to establish a hierarchal order on numerical sets(I.e. sets which contains numbers of limited properties). The ordinal infinity, instead, differentiates between finite and infinte sets, being infinity a property of a set, inasmuch it contains a number of elements such as no one is the bigger in regards to the operation which close that set(as you correctly indicate). You atre talking just of ORDINAL infinity. — Ikolos

All forms of infinity are impossible. The concept itself is fatally flawed, for example:

∞ + 1 = ∞ implies
1 = 0
Surely the mother of all proofs of contradictions. So infinity is not a mathematical concept. Maths models nature strongly suggest we will not find infinity in nature.

Actual Infinity is deeply illogical (see above, or as in the existence of an actually complete infinite set) whereas nature always follows logic, so again we will not find infinity in nature.

Believing in Actual Infinity is IMO akin to belief in magic. IE No place for it in science.

When you acknowledge Actual Infinity is impossible, the start of time follows logically.

time is the effect of our interaction with the physical world — Ikolos

Time is Time is fundamental to the universe. The speed of light speed limit (speed = distance / TIME) is obeyed by every particle in the universe and exists independently of change. To be a normally functioning universe, a speed limit is required. Else it's possible to accelerate objects to infinite velocity and thus straight out of the universe. So time is not emergent; it is fundamental to the universe.

But it is wrong to say: « Time is a series» for a mathematical series is n o t characterized by an o r i e n t a t i o n: you can go back and forth just the same. — Ikolos

Time is a series: Now (t=0) only exists because t=-1 had existence. t=-1 only exists because t=-2 had existence. So all moments must have a moment prior to them. The only topology that fits is a closed loop IE circular time.

Actual infinity, if it existed, would be a quantity greater than all other quantities, but:

There is no quantity X such that X > all other quantities because X +1 > X

The non-existence of actual infinity implies negative actual infinity does not exist. Negative actual infinity has the same structure as past eternal (in time):

{ …, 2015, 2016, 2017, 2018 }
{ …, -4, -3, -2, -1 }

IE past eternal (in time) is impossible. IE time had a start. The start is coincidental with the end; IE Circular time.

How else can you explain the Big Bang except the Big Crunch?

How about fractals with an infinite circumference and a finite area? — jorndoe

Fractals have a potentially infinite circumference (potentially depending on how many calculations we do). Fractals never have an Actually Infinite circumference.

Are you saying the equal sign means 'arbitrary close' rather than 'equals'?

Time is a series. You can't just arbitrary remove points from a series and the rest of the series remain intact. That's just common sense. Take away any moment in an object's life and the following moments are undefined.

Every moment must have a moment before it else its not valid. That's a self-evident axiom, and it implies time is circular.

It ties in with the physical evidence: The only place in the universe to get enough energy for the Big Bang is the Big Crunch so time must be circular.

Imagine an eternal being; he would have no start in time so could never exist. Being is possible we therefore conclude Eternal is not.

"We can always squeeze the fraction arbitrarily close to zero." — jorndoe

But arbitrarily close to zero is not zero and is never zero. The limit expression is always > zero.

Maths has a responsibility to make logical sense.

1/x = 0
Is false for all x (undefined for 0).

So writing
lim x->∞ 1/x = 0
is definitely wrong

1/x is always greater than 0 so it could lead to an error downstream.

Sometimes disciplines use specialized language because it's more precise and easier to deal with the technical nature of a topic, and knowledge consists of more than knowing the language that it happens to be written in — Moliere

But to write equals when something is not equals?

Mathematics should follow logic.

All I need is a grasp of the english language:

equal
adjective
the same in amount, number, or size

https://dictionary.cambridge.org/dictionary/english/equal

You are defending the indefensible. For something to be equal it has to be the same.

I don't see anything in the links to justify writing equal when something is plainly not equal.

Emotional pleasure/pain is a very broad category. I enjoy debating on line because the truth gives me pleasure for example. All my motivations likewise trace back to physical/emotional pleasure/pain. I am surprised that we are different.

but can travel arbitrarily fast depending on the direction — leo

But the universe is finite so we cannot have anything traveling at an infinite speed else it would not be in the universe.

You are avoiding my argument.

1/x = 0
Is false for all x (undefined for 0).

So writing
lim x->∞ 1/x = 0
is definitely wrong

lim x->∞ 1/x = 0
is an error.
For no value of x does 1/x take the value 0.

Time is fundamental because we can't have stuff flying around at infinite speeds in a sane universe. There has to be a speed limit so the universe must be time-aware. And all experimental evidence points to that speed limit.

If it's not a personal question, what motivates you?

I don't need to understand advanced calculus to point out an obvious notational error.

I remain convinced of the Special Theory of Relativity.

f we take existing ideas that are, at our current state of knowledge, unrelated, and we establish an unexpected (but useful! :wink:) connection between them, that connection is new and original. — Pattern-chaser

I agree the connection is new. But the existing idea traces its heritage to an older idea or directly to our senses. So inspiration seems to be providing those new links (via deduction or whatever).

Do you agree that without change there is no time? — leo

I see time as fundamental to the universe: The speed of light speed limit (speed = distance / TIME) is obeyed by every particle in the universe and exists independently of change. To be a normally functioning universe, a speed limit is required. Else it's possible to accelerate objects to infinite velocity and thus straight out of the universe. So time is not emergent; it is fundamental to the universe.

No idea.

Well I look at my routine. For example I put the trash out. Because it gives me pleasure to have a clean house. I go to bed on time because it gives me pleasure to wake up fresh in the morning, etc...

What are the drivers for you routine?

I do some things simply because it's routine for me — Terrapin Station

Your routine must reward you in some way else you would not do it. That reward counts as pleasure.

If someone did that, they wouldn't understand properly what a limit is and would be trying to get out of it something which it doesn't purport to be able to achieve — Mentalusion

So you agree we should write:
lim x->∞ 1/x ~ 0
rather than:
lim x->∞ 1/x = 0
?

That's because you seem unable to move beyond that which can be "deduced/adduced" — Pattern-chaser

How else do we derive new knowledge? It seems its always via links to existing knowledge (and ultimately to our senses).

I'm not saying its abduction/deduction only that we use, but whatever we use (heuristics etc...) it seems to take existing ideas as input.

For example, what's good for a bonobo might be evil for you — Pattern-chaser

But I have the same basic drivers as a bonobo; we both seek physical/emotional pleasure and shun physical/emotional pain.

That's clearly false off the bat — Terrapin Station

What drives you then if it is not physical/emotional pleasure/pain?

Good > evil? Don't be silly. :roll: The ">" sign only applies to quantities that can be numerically compared. Good and evil cannot be so enumerated — Pattern-chaser

But the only currency humans understand is physical/emotional pleasure/pain, so we can define:

good = pleasure > pain
evil = pain > pleasure

Good has more pleasure than evil. So we can say good>evil

No, I'm sorry, it isn't. Your 'proofs' are nothing but a list of dubious (i.e. unjustified) assertions, leading to an unjustifiable conclusion. — Pattern-chaser

Rather than saying I'm wrong, please say why I'm wrong (be specific).

Computer: input -> logic -> output
Us: senses->logic-> action

Everything we can deduce/adduce is from our senses. Our memory is filled with things deduced from our senses. I don't see where 'original thoughts' can come from?

You discount creativity, then? New ideas, even if they aren't truly original, as discussed, cannot be derived by deduction or induction. Creativity includes an element of chaos, randomness and disorder, and its output cannot always be understood in the logical/rational terms you present — Pattern-chaser

No-one so far has managed to come up with an example of a truly new idea; IE something that does not trace it's heritage to an old idea or observation.

As I said above, I believe we are like computers. A certain input generates a certain output. Computers can't generate truly original information so why should we be able to?

The question in the OP indicates that you don't know or don't understand the textbook definition. — SophistiCat

How so?

If you could provide an example of such an error that would make discussion a little easier — Mentalusion

What might happen is someone evaluates a limit and then they take the result as precise when it's only approximate. If it then depends critically whether this value is >, < or equals 0, then anything that includes the evaluation of a limit is suspect.

In the first case you can't say that the physical WORLD(as a whole) as a beginning whatsoever, because you must first account for the origin of the structure which made to you possible to distinguish two states at all, where a beginning would be the recognition of a thing in a certain state, within the recognition of the absence of any thing like that in a precedent state — Ikolos

The physical world (=universe) must have a temporal beginning. How can something exist without a temporal beginning? If you take away the Big Bang, the universe no longer exists. So deductively its impossible for the universe to exist without a temporal start.

I hope nobody thinks a hierarchy has a beginning, just as the laws that regulate the behavior of waves has none. — Ikolos

I would argue that everything real has a start, so a real world hierarchy has a start (eg the left leaf node). The laws of the universe, their start and end coincide with the start and end of the universe.

No. Look up the definition of the limit in any modern textbook or online reference. — SophistiCat

I know the textbook definition, the question the OP poses is: 'is the textbook definition correct?'.

So I think creation of 'new' ideas is more like filling in links. We start with an existing idea (which can be traced back to our senses) and what we create is the link to a new idea, via deduction/induction.

So its the deduction/induction is new and the premise always traces back to our senses?

But it's not possible to deduce/induce something from nothing. So an idea without a premise is impossible?

If it is derived, I'd say it is not truly original.

The problem being if you take the result =0 and use it somewhere else, you have lost the information that it never actually =0, if you see what I mean. That could lead to an error.

Yes. Going back to the computer analogy, our senses are the only input mechanism we have so all information must ultimately be traced back to something from our senses.