UR Consistent With Libertarian Free Will

[jriccitelli]

Is not 1/3, 1/3 of .999.... rather than 1/3 of 1.

[Michelle]

No, Timm. We are not talking about rounding here. We are speaking of EXACTNESS.
0.999... carried to a billion, a trillion, or a quadrillion places, or as many places as you wish, will always be less than 1. But we're talking here of an INFINITE number of places.

The following is not a proof, but it may help illlustrate the fact that 1 is EXACTLY equal to 0.999... (to an INFINITE number of decimal places.

⅓ = 0.333...
⅔ = 0.666...

Add the left sides and the right sides

⅓ = 0.333...
⅔ = 0.666...
1 = 0.999...

but, but, but...you can do that to make ANY number equal to 1

Say....12

⅓ = 4
⅔ = 8

Add the left sides and the right sides

1 = 12

Or say....300

⅓ = 100
⅔ = 200

Add the left sides and the right sides

1 = 300

[Paidion]

Is not 1/3, 1/3 of .999.... rather than 1/3 of 1.

⅓ can be ⅓ of 12 or ⅓ of 5280. It can be ⅓ of ANY number.

But being ⅓ of .999... is tantamount to being ⅓ of 1, since .999... and 1 are equal and can be regarded as two different symbols for the same number.
When one substitutes .999... for 1 in ANY calculation, the results are the same and are consistent.

3 + 1 = 4
3 + .999... = 3.999... = 4

I know that it is contrary to our intuition to see that .999... is equal to 1. I think the reason is that our minds cannot comprehend an infinite series of 9s after the decimal point.
Our brains insist on there being only a billion or a trillion or "eighty-twelve jillion" nines. In each of those cases, the decimal numeral is less than one. But with an infinite number of 9s after the decimal the decimal numeral is EXACTLY one.

[Paidion]

but, but, but...you can do that to make ANY number equal to 1

Say....12

⅓ = 4
⅔ = 8

Add the left sides and the right sides

1 = 12

When you make a logical or mathematical argument, your premises must be TRUE in order that the conclusion be true.

It is not true that ⅓ = 4 or ⅔ = 8, whereas in my original proof, the premises WERE true.

Also in my illustration to Timm (which you quoted), it is true that ⅓= .333... and ⅔= .666...

I don't know about United States, but in Canada every elementary school child (unless he's in special education) is taught this in grade 7.

[Michelle]

but, but, but...you can do that to make ANY number equal to 1

Say....12

⅓ = 4
⅔ = 8

Add the left sides and the right sides

1 = 12

When you make a logical or mathematical argument, your premises must be TRUE in order that the conclusion be true.

It is not true that ⅓ = 4 or ⅔ = 8, whereas in my original proof, the premises WERE true.

Also in my illustration to Timm (which you quoted), it is true that ⅓= .333... and ⅔= .666...

I don't know about United States, but in Canada every elementary school child (unless he's in special education) is taught this in grade 7.

OOOHHH

OOOPS!

I totally misread what you said (I think I might have been influenced by reading JR's post first.) I'm sorry. I'll read more carefully from now on.

[Paidion]

No problem, Michelle.

[RICHinCHRIST]

I know that it is contrary to our intuition to see that .999... is equal to 1. I think the reason is that our minds cannot comprehend an infinite series of 9s after the decimal point.
Our brains insist on there being only a billion or a trillion or "eighty-twelve jillion" nines. In each of those cases, the decimal numeral is less than one. But with an infinite number of 9s after the decimal the decimal numeral is EXACTLY one.

This logic makes sense to me. When infinitude is involved, the results are identical. In the same way, if one has an infinite amount of opportunities for repentance, then eventually they will repent. The only question is whether God is willing to give infinite chances to people. I don't see why He would not.

[mattrose]

I know that it is contrary to our intuition to see that .999... is equal to 1. I think the reason is that our minds cannot comprehend an infinite series of 9s after the decimal point.
Our brains insist on there being only a billion or a trillion or "eighty-twelve jillion" nines. In each of those cases, the decimal numeral is less than one. But with an infinite number of 9s after the decimal the decimal numeral is EXACTLY one.

This logic makes sense to me. When infinitude is involved, the results are identical. In the same way, if one has an infinite amount of opportunities for repentance, then eventually they will repent. The only question is whether God is willing to give infinite chances to people. I don't see why He would not.

I, on the other hand, still disagree with both the illustration and the point taken from it.

.999... is not equal to 1. it is just as similar as possible without being equal.

If one has an infinite amount of opportunities for repentance, they have an infinite amount of opportunities to make a free will decision. Free will decisions are, by definition, free of certainties. The illustration/point also doesn't factor in the fact that people are not in 'neutral' just getting chance after chance to repent. We are either softening or hardening our heart at all times. Theoretically, it could become less and less likely for someone to repent post death (especially if they eventually cease to exist).

Then again, I have simply come back into this thread to make the same point I made earlier

[Singalphile]

I hadn't been reading the thread, but I popped in and saw all this math, so I had to go see what ya'll were talking about.

I scanned wikipedia's page about it. If I understood it correctly, .99999... (infinite 9's) is indeed another way of writing 1. So .9999... = 7/7 = 1. Just different ways of expressing/writing the same number.

What that has to do with free will or UR? 0

[steve7150]

We are either softening or hardening our heart at all times. Theoretically, it could become less and less likely for someone to repent post death (especially if they eventually cease to exist).






That's assuming that the heart condition must continue to progress in a linear one way direction. I would think there are many exceptions to this assumption.