Philosophy Now Forum

devans99 wrote: ↑Tue Nov 27, 2018 2:20 pm Say I evaluate:

lim x->∞ 1/x ~> 0

the notation ~> preserves the fact that the expression approaches zero from above.

If I were to then use the above result in another deduction, I would not make an erroneous follow-on error of assuming it equalled zero.

Does it tell you from which side it's approaching 0? Don't think so.

lim x->∞ (2/x) > lim x->∞ (1/x) for x > 0
lim x->∞ (2/x) - lim x->∞ (1/x) > 0 for x > 0


lim x->∞ (2/x - 1/x) > 0 for x > 0
lim x->∞ (1/x) > 0 for x > 0

1/x > 0 for x > 0

That's a tautology.

Also if we do the same for -1/x it approaches 0 from the other side. So... you've gained nothing.

I think you are fighting to preserve your use of infinity-limits

In the real world - as we continue to approach zero we are left with either an event or not an event - the binary finality to the 'infinitely' small.

In the world of mathematics you get to be a hypocrite or a pragmatist. Make your choice

Chasing the LNC is harmful idealism.

I see no inconsistency in my use of approximately equals. Calculus would be better off if it adopted this approach IMO.

Now that we've eliminated Actual Infinity, that implies negative Actual Infinity does not exist which has exactly the same structure as past eternity:

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

Neither have a start so they are both only partially defined. IE they are undefined. Eternity can't exist so time must have a start.

devans99 wrote: ↑Tue Nov 27, 2018 2:31 pm I see no inconsistency in my use of approximately equals. Calculus would be better off if it adopted this approach IMO.

I see ambiguity in your use of "~=".

A = B
A < B
A > B

A ~= B is covered in the above FOR ALL REAL NUMBERS.

If you believe otherwise, show me a falsifier.

TimeSeeker wrote: ↑Tue Nov 27, 2018 2:29 pm In the world of mathematics you get to be a hypocrite or a pragmatist. Make your choice

Chasing the LNC is harmful idealism.

Since we are talking about whether the universe can be infinite, I am going with pragmatist - in that 'matter' has a finite point - either an event or not an event, at it most finite (small) point.

attofishpi wrote: ↑Tue Nov 27, 2018 2:35 pm Since we are talking about whether the universe can be infinite, I am going with pragmatist - in that 'matter' has a finite point - either an event or not an event, at it most finite (small) point.

Agreed, but the moment you USE an infinity in your equation you have violated the laws of logic and are resorting to heuristics.
Like I said earlier - admirable and pragmatic! But if you want to be a purist and pretend to adhere to the LNC, such hypocrisy will bite you in the ass

This universe has no room for idealists.

TimeSeeker wrote: ↑Tue Nov 27, 2018 2:32 pm

devans99 wrote: ↑Tue Nov 27, 2018 2:31 pm I see no inconsistency in my use of approximately equals. Calculus would be better off if it adopted this approach IMO.

I see ambiguity in your use of "~=".

A = B
A < B
A > B

A ~= B is covered in the above FOR ALL REAL NUMBERS.

If you believe otherwise, show me a falsifier.

Well for the '~' to be complete, we need to decide what level of precision constitutes approximately. I've suggested that we just use it for limits, IE arbitrarily high precision.

devans99 wrote: ↑Tue Nov 27, 2018 2:40 pm Well for the '~' to be complete, we need to decide what level of precision constitutes approximately. I've suggested that we just use it for limits, IE arbitrarily high precision.

How?

https://en.wikipedia.org/wiki/Decision_problem

All decision problems which are not algorithmic (deductive) require a value judgment.

Like I said earlier. ANY use of the ~= symbol incurs the precision-range trade-off.
https://en.wikipedia.org/wiki/Floating-point_arithmetic

TimeSeeker wrote: ↑Tue Nov 27, 2018 2:40 pm

devans99 wrote: ↑Tue Nov 27, 2018 2:40 pm Well for the '~' to be complete, we need to decide what level of precision constitutes approximately. I've suggested that we just use it for limits, IE arbitrarily high precision.

How?

https://en.wikipedia.org/wiki/Decision_problem

All decision problems which are not algorithmic (deductive) require a value judgment.

Like I said earlier. ANY use of the ~= symbol incurs the precision-range trade-off.
https://en.wikipedia.org/wiki/Floating-point_arithmetic

This is off topic and you are not making sense. How? We simply adopt it as a mathematical notational convention.

devans99 wrote: ↑Tue Nov 27, 2018 2:51 pm This is off topic and you are not making sense. How? We simply adopt it as a mathematical notational convention.

It is not off-topic.

How many digits do you propose is "approximate enough" for 1 ~= 1?

5? 10? 100? 1000? 1000000? 100000000000000000? 1000000000000000000000000000000000000000000000000000000000000000000000?

How would we decide on this magical number?

TimeSeeker wrote: ↑Tue Nov 27, 2018 2:53 pm

devans99 wrote: ↑Tue Nov 27, 2018 2:51 pm This is off topic and you are not making sense. How? We simply adopt it as a mathematical notational convention.

It is not off-topic.

How many digits do you propose is "approximate enough" for 1 ~= 1?

5? 10? 100? 1000? 1000000? 100000000000000000?

How would you decide?

It's a potentially infinite number of digits. It's only for use with limits which become arbitrarily close to a given value.

devans99 wrote: ↑Tue Nov 27, 2018 2:54 pm It's a potentially infinite number of digits. It's only for use with limits which become arbitrarily close to a given value.

Weasel words!

How many digits makes 1 ~= 1?

Like I said its potentially infinite number of digits. IE it has to be approximately equal to arbitrarily high precision. So that is no fixed number of decimal places.

devans99 wrote: ↑Tue Nov 27, 2018 2:58 pm Like I said its potentially infinite number of digits. IE it has to be approximately equal to arbitrarily high precision. So that is no fixed number of decimal places.

Infinite number of digits? How does that work if infinities are only potential not real?

You are just trying to sneak infinity through the back door again!