Choose a natural number as large as you can. Afterwards you can choose a larger natural number. Why couldn't you choose this number before? What
is the reason that this holds for every choice?
Regards, WM
On 3/3/24 2:29 PM, WM wrote:
Choose a natural number as large as you can. Afterwards you can choose
a larger natural number. Why couldn't you choose this number before?
What is the reason that this holds for every choice?
Regards, WM
Why SHOULD we choose the highest possible number?
Since every Natural Number has a higher number, of course we can always
find a Higher number, that just comes out of the definition of the
Natural Numbers, EVERY Natural number has a successor, so there is aways
a choice for a higher number.
On 03.03.2024 21:57, Richard Damon wrote:
On 3/3/24 2:29 PM, WM wrote:
Choose a natural number as large as you can. Afterwards you can
choose a larger natural number. Why couldn't you choose this number
before? What is the reason that this holds for every choice?
Regards, WM
Why SHOULD we choose the highest possible number?
It would be a good exercise to see that not all numbers are available.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Since every Natural Number has a higher number, of course we can
always find a Higher number, that just comes out of the definition of
the Natural Numbers, EVERY Natural number has a successor, so there is
aways a choice for a higher number.
But if the set ℕ is complete and no number is missing, why cannot every number of ℕ be chosen at the first try?
Regards, WM
On 3/3/24 4:40 PM, WM wrote:+
On 03.03.2024 21:57, Richard Damon wrote:
On 3/3/24 2:29 PM, WM wrote:
Choose a natural number as large as you can. Afterwards you can
choose a larger natural number. Why couldn't you choose this number
before? What is the reason that this holds for every choice?
Why SHOULD we choose the highest possible number?
It would be a good exercise to see that not all numbers are available.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
No, because if we TRY to pick the "highest" number, we find there is no
such number, because there is always a higher.
But if the set ℕ is complete and no number is missing, why cannot
every number of ℕ be chosen at the first try?
We CAN choose every number, there just isn't a highest.
Choose a natural number as large as you can. Afterwards you can choose
a larger natural number. Why couldn't you choose this number before?
What is the reason that this holds for every choice?
On 2024-03-03 19:29:42 +0000, WM said:
Choose a natural number as large as you can. Afterwards you can choose
a larger natural number. Why couldn't you choose this number before?
What is the reason that this holds for every choice?
Lack of exercise.
On 03.03.2024 22:53, Richard Damon wrote:
On 3/3/24 4:40 PM, WM wrote:
On 03.03.2024 21:57, Richard Damon wrote:
On 3/3/24 2:29 PM, WM wrote:
+Choose a natural number as large as you can. Afterwards you can
choose a larger natural number. Why couldn't you choose this number
before? What is the reason that this holds for every choice?
Why SHOULD we choose the highest possible number?
It would be a good exercise to see that not all numbers are available.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
No, because if we TRY to pick the "highest" number, we find there is
no such number, because there is always a higher.
We do not try to pick the highest number. The question is: Why can't we
pick immediately what we can pick later?
But if the set ℕ is complete and no number is missing, why cannot
every number of ℕ be chosen at the first try?
We CAN choose every number, there just isn't a highest.
But we cannot choose in the first attempt what we can choose in the
second or third. What is the reason if not potential infinity, i.e., non permanent existence of numbers?
Regards, WM
On 3/4/24 3:58 AM, WM wrote:
Why can't we
pick immediately what we can pick later?
We could have if we wanted.
Who says you couldn't?
We CAN choose every number,
But we cannot choose in the first attempt what we can choose in the
second or third. What is the reason if not potential infinity, i.e., non
permanent existence of numbers?
Again, why couldn't you choose that number first? What stopped you.
Your LATER sets of numbers have restrictions, that they can't be too
low, but nothing stopped you from choosing that higher number first.
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