You said points have no size. I do not see how any part of time could have no size. If it has no size, then no time is passing at that "point", therefore it is not part of time. The same principle holds for space. If it has no size, then it cannot be part of spatial existence, because there is no space there. It is very clear to me, that if points have no size, then they are excluded from space and time, because things existing in space and time have size. Having size is what makes them spatial-temporal. Do you not understand this? — Metaphysician Undercover
Of course definitions can be contradictory. That's why they matter. In this context this means this, and in that context this means that. What's ridiculous is someone who doesn't get that and (apparently) insists that if this mean this for this,then it cannot mean that for that.What's ridiculous is that people like you refuse to accept the obvious, and keep touting your contradictory definitions. — Metaphysician Undercover
Some perfectly sensible and familiar rational numbers, such as 1/3 = .3333333..., have infinitely-long decimal representations. — fishfry
Of course definitions can be contradictory. — tim wood
↪Magnus Anderson I can't even hazard a guess as to how you think "most people" define "0.333~" (I am more accustomed to the ... notation, but I assume you mean the same thing). — SophistiCat
[math] \displaystyle\frac{1}{3} = \displaystyle\sum_{n \in \mathbb{N}} \frac{3}{10^n} = 0.333\cdots [/math] where [math]\mathbb{N}[/math] does not include [math]0[/math]
Now people are saying objects have no size. Oh boy! — Gregory
There are only two classes of people who need to carefully make this distinction: mathematicians, who are trained on this topic in their undergrad years; and philosophers, — fishfry
Zenos paradox shows the infinity within the finitude of objects. The fact we can break a candy bar in two shows this applies to our world. That is enough for banach tarski. You can take infinity out of infinity. The extra cantor stuff well extra — Gregory
"0.333~" represents the infinite sum 3 x 1 / 10^1 + 3 x 1 / 10^2 + 3 x 1 / 10^3 + ... + 3 x 1 / 10^inf. It does not represent its limit. — Magnus Anderson
Likewise anyone can see that objects in the world are both finite and infinite. — Gregory
surveyor places a stake as a marker/point for a property line. Being dimensionless, you can't see it, but an object is provided in the form of a marker, blob of medium on a surface, pixel on a screen. — sandman
I think we can know what an orange is, and that it doesnt have less volume when cut in half. It can be so divided infintely, so it's infinite AND finite. This is so obvious — Gregory
But there is no way to mark an exact irrational length on the ruler - unless a line representing an irrational distance is constructed (like the square root of two) and marked on the ruler by direct measurement. Correct? — tim wood
Continuum is a set of points where for every two points in the set there exists a point in the set that is in between the two points. — Magnus Anderson
Incidentally, your compact form of Leibnitz expansion has a simple error. And 1/3 =.333... = limit of a geometric series, well defined. You may be talking about mathematicians who labour in foundations. Making such fine distinctions is unnecessary in most math careers, IMHO. — jgill
I don't see why Zeno's paradox is not a paradox but Banach-Tarski is. — Gregory
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