Philosophy Now Forum

devans99 wrote: ↑Tue Nov 27, 2018 1:32 pmYes.

OK cool. So.

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

since we never actually evaluate FOR infinity (that's illegal) then:

at x = 0.01 -> 200 ~= 100
at x = 1 -> 2 ~= 1
at x = 99999999999999 then 0,0000000002 =~ 0,0000000001

Is this correct?

Maths is the only form that infinities exist, and as a form of convenience.

attofishpi wrote: ↑Tue Nov 27, 2018 1:39 pm Maths is the only form that infinities exist, and as a form of convenience.

Yes. But You have to listen to his post-hoc justification

He rejects infinities BUT..... he wants to use them for limits

And he objects to being called a hypocrite for engaging in a performative contradiction.

TimeSeeker wrote: ↑Tue Nov 27, 2018 1:40 pm

attofishpi wrote: ↑Tue Nov 27, 2018 1:39 pm Maths is the only form that infinities exist, and as a form of convenience.

Yes. But You have to listen to his post-hoc justification

He rejects infinities BUT..... he wants to use them for limits

Sure, but I am confused after the 3rd smiley.

TimeSeeker wrote: ↑Tue Nov 27, 2018 1:39 pm

devans99 wrote: ↑Tue Nov 27, 2018 1:32 pmYes.

OK cool. So.

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

since we never actually evaluate FOR infinity (that's illegal) then:

at x = 0.01 -> 200 ~= 100
at x = 1 -> 2 ~= 1
at x = 99999999999999 then 0,0000000002 =~ 0,0000000001

Is this correct?

Just because two functions are equal as x tends to infinity does not mean they are equal for other values of x, as your calculation shows.

devans99 wrote: ↑Tue Nov 27, 2018 1:42 pm Just because two functions are equal as x tends to infinity does not mean they are equal for other values of x, as your calculation shows.

But they are NOT equal as x tends to infinity!!!!!!

If they were equal you would have said:

lim x->∞ (1/x) = 0
lim x->∞ (2/x) = 0

Instead you CHOSE to say;

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

Does = mean the same thing as ~= now ?!?!?!?

The two functions are approximately equal when x tends to infinity. They are not not equal for any other value of x.

devans99 wrote: ↑Tue Nov 27, 2018 1:46 pm The two functions are approximately equal when x tends to infinity. They are not not equal for any other value of x.

What does "approximately equal" mean?!? Things are either equal, smaller or larger than each other!

When dealing with real numbers only one of these is true!

A = B
A < B
A > B

What the hell does A ~=B mean ?!?!?!?

TimeSeeker wrote: ↑Tue Nov 27, 2018 1:50 pm

devans99 wrote: ↑Tue Nov 27, 2018 1:46 pm The two functions are approximately equal when x tends to infinity. They are not not equal for any other value of x.

What does "approximately equal" mean?!? Things are either equal, smaller or larger than each other!

ONLY ONE OF THESE IS TRUE:

lim x->∞ (2/x) = lim x->∞ (1/x)
lim x->∞ (2/x) < lim x->∞ (1/x)
lim x->∞ (2/x) > lim x->∞ (1/x)

What the hell does this mean !?!?
lim x->∞ (2/x) ~= lim x->∞ (1/x)

What the hell does ~= mean ?!

lim x->∞ (2/x) ~= lim x->∞ (1/x)
Both expressions tend to zero as x tends to infinity. But at no point on the way to infinity are the two expressions equal. So we write approximately equal.

We can also write
2/x > 1/x for all x except 0.

So maybe its best to write:

lim x->∞ (2/x) >~ lim x->∞ (1/x)

So '>~' denotes its approximately equal with 1/x always being less than 2/x.

devans99 wrote: ↑Tue Nov 27, 2018 1:56 pm lim x->∞ (2/x) ~= lim x->∞ (1/x)
Both expressions tend to zero as x tends to infinity. But at no point on the way to infinity are the two expressions equal. So we write approximately equal.

We can also write
2/x > 1/x for all x except 0.

So maybe its best to write:

lim x->∞ (2/x) >~ lim x->∞ (1/x)

So '>~' denotes its approximately equal with 1/x always being less than 2/x.

Sorry. No can do. This is special pleading.

lim x->∞ (2/x) lies on the real number line, does it not?
lim x->∞ (1/x) lies on the real number line, does it not?

A = B
A < B
A > B

Can ALWAYS be determined for any two real numbers, and since we never actually evaluate AT infinity itself then I will settle for nothing less than:
lim x->∞ (2/x) > lim x->∞ (1/x) for x > 0
lim x->∞ (2/x) < lim x->∞ (1/x) for x < 0

TimeSeeker wrote: ↑Tue Nov 27, 2018 1:59 pm

devans99 wrote: ↑Tue Nov 27, 2018 1:56 pm lim x->∞ (2/x) ~= lim x->∞ (1/x)
Both expressions tend to zero as x tends to infinity. But at no point on the way to infinity are the two expressions equal. So we write approximately equal.

We can also write
2/x > 1/x for all x except 0.

So maybe its best to write:

lim x->∞ (2/x) >~ lim x->∞ (1/x)

So '>~' denotes its approximately equal with 1/x always being less than 2/x.

Sorry. No can do. This is special pleading.

lim x->∞ (2/x) lies on the real number line, does it not?
lim x->∞ (1/x) lies on the real number line, does it not?

A = B
A < B
A > B

Can ALWAYS be determined for any two real numbers, and since we never actually evaluate AT infinity itself then I will settle for nothing less than lim x->∞ (2/x) > lim x->∞ (1/x)

But its possible for BOTH of the following to be true at the same time:

A > B
A ~ B

So you see the advantage to the '>~' notation?

devans99 wrote: ↑Tue Nov 27, 2018 2:02 pm A ~ B

Can you give me a value of X for which A ~ B is true ?

TimeSeeker wrote: ↑Tue Nov 27, 2018 2:03 pm

devans99 wrote: ↑Tue Nov 27, 2018 2:02 pm A ~ B

Can you give me a value of X for which A ~ B is true ?

A ~ B
1 ~ 1

For example.

devans99 wrote: ↑Tue Nov 27, 2018 2:10 pm 1 ~ 1

Can you explain what this adds over and above =, < and > when dealing with real numbers?

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.