Philosophy Now Forum

commonsense wrote: ↑Wed Nov 27, 2019 6:28 pm Numbers are grounded in counting ones, not zeros. We count [1]’s. Zero counts as no [1]’s.

Why would it matter? Why couldn't I just count zeros?

0, 00, 000, 0000, 00000, ...

Works just as well as 1's, right?

Speakpigeon wrote: ↑Sat Nov 09, 2019 10:17 am Are there propositional logic formulas, outside self-referential ones, whose validity or invalidity is often perceived as counter-intuitive?
EB

https://xkcd.com/179/

I wonder why you insist I've made any error given that I never made any such claims in context of Turing's conception/definition? YOU brought that to the table. Not me. You made the claim that .999... will "never halt." By that (stupid) criterion NO real number is computable. Hence my obs...

The fact that you are talking about numbers (they don't exist!) and not alphabets , is only more evidence that you don't understand that Mathematics is just a formal language. Notation is all. I wonder why you won't address your error in claiming .999... is not a computable real number; and your to...

Skepdick wrote: ↑Tue Oct 22, 2019 9:24 pm In the bin.

You totally misunderstand everything Turing said. It's pathetic. Flap your arms and throw insults if it makes you feel better.

It is obvious then than sigma(n) = 0.99999999999999999... It is also obvious that sigma(∞) DOES NOT HALT Let me explain exactly the problem I have with your line of argument. It's not that you don't understand standard math. It's that you don't even understand computable math , which you claim to b...

You are using "..." in the definition of "...". Isn't that circular reasoning? No, since the ellipses are not the point at issue here. Surely you know that. I found this remark disingenuous because of that. Rather we are interested in the precise definition of decimal notation. ...

.9999... goes on ad infinitum...get over your mystic religion. The proof is assumed because it cannot be seen in it totality. The proof cannot be seen in its totality. The proof that .999... = 1 can be seen in its totality in any calculus class; in any calculus textbook; on the Wiki page for the ge...

No, it is assumed. Everything you said in this post is incorrect so I won't bother to fix up your deliberately obfuscated markup. The moment you find yourself using the color tag, why not just use the standard quoting tags like everyone else? You would benefit greatly from reviewing your basic high...

If .999999999.... equals 1 does .0000....0001 = 0? No, the notation on the right is not defined. The notation on the left .999..., is defined as 9/10 + 9/100 + 9/1000 + ... which is a geometric series that sums to 1, as is proved in freshman calcuus the world over. https://en.wikipedia.org/wiki/Geo...

Eodnhoj7 wrote: ↑Fri Oct 18, 2019 8:15 pm Whatever is charted is rounded. If the number is truly charted, the line would slowly change because it would be dynamic.

Can you plot 1/3 = .3333... on the number line?

How about 1/2 = .4999999....?

Irrational numbers cannot be marked on a number line as that would make them rational and finite....they would have to be rounded and in a fixed postion. That's silly. Take a square of side 1. Its diagonal has length sqrt(2). That's a fixed, unchanging length of sqrt(2). You could translate the dia...

Ignore the red, I messed up and forgot you posted in read. Sorry, you are going to have to sort it out...I am using an ipad. It's all red. I never posted in red. YOU posted in red and I had to sort it out. I'll take a look at what you wrote but meanwhile the quote tags are very straightforward on t...

So points have a distance between them but this distance has no length? That is a contradiction. I said you can call the distance a length if you like. That's exactly what I said. Formally, in the theory of metric spaces, we assign a distance between any two points. If you like, you may informally ...

I never asked if the points have zero length, I asked if more than one point always constitutes a length No. Two points may have a distance between them. They don't "constitute" a length, that doesn't mean anything. But two points (in a metric space such as the real numbers) always have a...