https://xkcd.com/179/Speakpigeon wrote: ↑Sat Nov 09, 2019 10:17 amAre there propositional logic formulas, outside self-referential ones, whose validity or invalidity is often perceived as counter-intuitive?

EB

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- Sun Nov 10, 2019 10:48 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Counter-intuitive formulas?
- Replies:
**3** - Views:
**85**

### Re: Counter-intuitive formulas?

- Tue Oct 22, 2019 10:28 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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 observation t...

- Tue Oct 22, 2019 10:16 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Tue Oct 22, 2019 9:40 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

- Tue Oct 22, 2019 9:06 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Tue Oct 22, 2019 12:55 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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. If this site support...

- Sat Oct 19, 2019 1:03 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

.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...

- Fri Oct 18, 2019 11:50 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Fri Oct 18, 2019 11:34 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Fri Oct 18, 2019 10:01 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

- Fri Oct 18, 2019 7:02 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Fri Oct 18, 2019 7:21 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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...

- Fri Oct 18, 2019 5:35 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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 ...

- Fri Oct 18, 2019 4:45 am
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

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 distance ...

- Thu Oct 17, 2019 9:10 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: 0d Lines and Circles
- Replies:
**201** - Views:
**2697**

### Re: 0d Lines and Circles

So if a line is length between two points, and a line is composed of infinite points, a line is composed of infinite lengths? A line is composed of infinitely many points, each of which has zero length. Yet a line has nonzero length. This is a mystery, but we have mathematical formalisms to deal wi...