After lengthy process of "deep learning" and back propagation of information; would we get static coefficients for the thousand of nodes; for example for playing game of chess, would that state be good to hard-wire on the silicon cheep and this way we would have perfect chess player?
Or the...
count(ℝ) > count(ℚ) ; count(ℚ) == count(ℕ)
But still in-between any members of ℝ, we are quarantine to find element of ℚ
Can someone help me understand: were are these members of ℝ we cannot account for?
For reference: https://en.wikipedia.org/wiki/Rational_number
"The rationals are a dense...
Thank you - I miss it, it is getting worst and worst for us humans, we all are finite set and what we recognized you event cannot see and "touch" - if you point with "Platonic" needle , you will never touch "known numbers" (0 probability) no matter how small the segment and how much it was...
I guess I mean: https://en.wikipedia.org/wiki/Lebesgue_measure , but i remember geometric explanation: the cross of segment and ℝ. If you select point in space below the height of segment cross , you can draw straight line crossing segment and infinite line, and then you have one to one relation...
Let me rephrase my question: If we resale all numbers into segment [0,1] (like 0.314156535..., 0.2, 0.3, 0.17)
Remove all numbers from the set: defined as [p/q] p,q ∈ N and q≠ 0 (as far as I remember it has ℂ cardinality, (all primes are gone, for example) only 0.314155635 will stay from my...
I am living in the Platonic world. If you believe Cantor any set of all subset of the set has next-step aleph-n carnality.
Segment has carnality of space if we count as my profesor at high-school defined: to buckets we remove elements for each if they are both empty they equal (Lebasgue ?)...
I rest my case it is other way around , basically it is infinitely less than I thought and ascribed to people knowledge.
The number we named , recognized , get from any equation ever written is < than aleph-0 , it is finite number,
oh well so much still to discover.
At last the number of...
1)
ℕ number of people in history each named , recognized ℕ numbers.
Because ℕ x ℕ is still ℕ and count of ℕ is Aleph-0 , I dare to say that my question still stands?
1)
Can I say that humans in history named, recognized countable set of numbers (1,2..Pi,sqrt(2) ... etc)
the count of this set is named aleph-0 ?
2)
Do mathematicians investigate the "other" continuum set of numbers which is infinity bigger ?
Do we suspect, knows anything about that set like...
Thank you very much, this is exactly what I was asking for. Believing or not this is surprising answer (expected much more digits!) . Now when I think about it, the difficulty lies in measuring Universe with such a precision.
Thank you-
3) @fresh_42 looking at the beautiful book the Zoomable Universe, we have 10^27 Universe and 10^-18 field scale , on next page is Pi ;) - my question was how can we figure out to measure 10^27 with resolution 10^-18 for example (not a Planck but BIGGER) , how many digits of Pi we...
1) If Pi has my birthday digit sequence starting at digit at ~ 200k position (I did check, strange experience), can It also contain digital encoded (Ascii) Shakespeare's Hamlet? or Any other human creation ever done now and in the future?
2) Pi square ~ 9.86960440109 , we can calculate...
I am sorry, what I was trying to ask is if it is possible that there maybe parallel Universe(s) "so close" less than Plank length? It is so far unreachable for us ; as you have mentioned before - energy level to observe it. Prof Saskind in War of Black Holes mentioned some experiments pointing...
thank you very much -- I am just speculating here, so any answer makes me happy
a) I guess for the local observer Plank length is Plank length, am I wrong?
b) I thought that there will be more objections to the corners (the surface is not smooth, my understanding is weak even in the sense of JR...