Philosophy Now Forum

devans99 wrote: ↑Tue Nov 27, 2018 11:58 am ∴ 1/x = ~0/x
∴ 0 = ~0

You need to show the steps in between

∴ 1/x = ~0/x
∴ 0 = ~0

As x->∞

All correct

devans99 wrote: ↑Tue Nov 27, 2018 12:01 pm ∴ 1/x = ~0/x
∴ 0 = ~0

As x->∞

All correct

No darling.

If lim(A) = lim(B)
∴ A = B

lim x->∞ (1/x) = lim x->∞ (~0/x)
∴ 1/x = ~0/x

What you have written makes no sense. You are not going to prove 1=0 no matter how hard you try.

devans99 wrote: ↑Tue Nov 27, 2018 12:05 pm What you have written makes no sense. You are not going to prove 1=0 no matter how hard you try.

Listen snowflake.

These are YOUR AXIOMS.
Such are their consequences!

Find the error or acknowledge the contradiction!

I am NOT proving 1 = 0 (this is your strawman)

I am PROVING that 1 = ~ 0

It's your axiom that infinity exists.

∞ + 1 = ∞
1 = 0

It's your contradiction, not mine.

devans99 wrote: ↑Tue Nov 27, 2018 12:09 pm It's your axiom that infinity exists.

∞ + 1 = ∞
1 = 0

It's your contradiction, not mine.

Lol. Denial is not just a river in Africa it seems.

Remember this post?

TimeSeeker wrote: ↑Tue Nov 27, 2018 11:09 am Listen. In this entire exercise you are appealing to consistency. You are following the law of non-contradiction it seems.
Forget my argument - you are missing far too much background knowledge to get to my position.

Instead - I'll just drive you to a contradiction in your own position and leave you befuzzled to figure out how you got there.

You said lim x-> ∞ 1/x = ~0

Can you tell me what 1 * ~0 = ?

It's like I PREDICTED what will happen! Magic!

I didn't contradict ∞ + 1 = ∞. I asked you to forget it entirely.

I contradicted YOUR AXIOMS!!!!
lim x->∞ (1/x) = ~0
lim x->∞ (~0/x) = ~0

Do you remember when I told you that you are a hypocrite for even USING infinities. and you said "potential infinities are OK.". And I said 'No they aren't"?

Let me remind you. It happened over here:

TimeSeeker wrote: ↑Sun Nov 25, 2018 9:33 pm Do you reject mathematical equations which contain the symbol ∞ ? Asymptotic functions e.g lim x->∞ f(x) = 1

If you don't - you are a hypocrite.

devans99 wrote: ↑Sun Nov 25, 2018 9:42 pm Not limit statements. Taking the limit as x tends to infinity can be defined purely in terms of potential infinity. The chief problem with taking a limit is that as actual infinity is never achieved (that's impossible) so a limit is by definition an approximation. So I'd suggest the use of the ~ rather than = as in:

lim 1/x as as >∞ ~ 0

Small errors like writing the above as = 0 can cause discrepancies further down the line. The use of the approximately equals sign helps to guard against such errors.

So now I have contradicted your limit statements AND demonstrated your hypocrisy to the world and you are just flopping like a fish out of water.

I think I am supposed to let you save face and preserve some dignity about here...

There is no contraction. You just made an error evaluating a limit and erroneously arrived a 1=0.

devans99 wrote: ↑Tue Nov 27, 2018 12:27 pm There is no contraction. You just made an error evaluating a limit and erroneously arrived a 1=0.

Extraordinary claims require extraordinary evidence.

Show me evidence of error.

TimeSeeker wrote: ↑Tue Nov 27, 2018 11:38 am

devans99 wrote: ↑Tue Nov 27, 2018 11:20 am lim x->∞ ~0/x =~ 0

Actually! I look here/

lim x->∞ (1/x) = ~0 (2)
lim x->∞ ~0/x = ~0 (3)


****************
lim x->∞ (1/x) = lim x->∞ ~0/x


**
1 = ~ 0

CONTRADICTION

Look where I've highlighted the error in the above post with asterisks. lim x->∞ (1/x) is 0 not 1.

devans99 wrote: ↑Tue Nov 27, 2018 12:27 pm There is no contraction. You just made an error evaluating a limit and erroneously arrived a 1=0.

devans99 wrote: ↑Tue Nov 27, 2018 12:31 pm Look where I've highlighted the error in the above post with asterisks. lim x->∞ (1/x) is 0 not 1.

Strawman. Here is the full contradiction.


### Limit laws
lim(A) = lim(B)
∴ A = B


AXIOMS:
lim x->∞ (1/x) = ~0
lim x->∞ (~0/x) = ~0

From limit laws:
lim x->∞ (1/x) = lim x->∞ (~0/x)
∴ (1/x) = (~0/x)
∴ 1 = ~0

School's out for today.

What happened to you is you fell for the range-precision trade-off when dealing with floatingpoint arithmetic.
https://en.wikipedia.org/wiki/Floating-point_arithmetic

the lim x-> ∞ (1/x) = 0.0000000000000000000000000000000000000000<......∞.........>1

You gave up precision (by inventing ~0 - which is wrong in exactly the same way ∞ is wrong) and then it bit you in the ass.

lim x->∞ (1/x) = lim x->∞ (~0/x)
∴ (1/x) = (~0/x)
∴ 1 = ~0

Just because something is equal in the limit, does not mean it is equal for all instances of x.

If I set x=2 then (1/x) = (~0/x) equal 1/2 ~ 0 which is nonsense.

Its only when I set x=∞ that we can say:

lim x->∞ (1/x) ~= lim x->∞ (~0/x)

All it implies is

0 ~= 0

For example:

lim x->∞ (1/x) = lim x->∞ ( 2/x)

But in general:

1/x <> 2/x

devans99 wrote: ↑Tue Nov 27, 2018 12:38 pm lim x->∞ (1/x) = lim x->∞ (~0/x)
∴ (1/x) = (~0/x)
∴ 1 = ~0

Just because something is equal in the limit, does not mean it is equal for all instances of x.

If I set x=2 then (1/x) = (~0/x) equal 1/2 ~ 0 which is nonsense.

Its only when I set x=∞ that we can say:

lim x->∞ (1/x) ~= lim x->∞ (~0/x)

All it implies is

0 ~= 0

Apologetics

You just don't know when to stop digging, do you?

What does '~= ' mean ?