/sci/ - Science & Math

>>7975744
Have you watched Wildburgers videos?

Anyway, what you say doesn't work:
Take the sequence you defined and consider the new sequence
[math] V_n := U_n [/math] for n not 74
and
[math] V_{74} := -28 [/math].

This new sequence has the same limit but is different from the other "real number". You get too many terms in your theory of real numbers.
People thus pull up the autistically large framework of set theory so they can define reals as equivalence classes of such sequences.
Okay, then take this equivalence class definition of the reals.

Consider a sequence [math]W_n[/math] which for the first d=10^10^10^10^10^10^10^10 numbers are some random natural numbers and after [math]W_d[/math] you have [math]W_k:=U_k[/math]. Hence [math]W_n[/math] converges to your root two and thus is a representative of that equivalence class. However, if you had someone the sequence [math]W_n[/math] and ask him what number it represents, he can't tell you, because all that's accessible to him is random gibberisch. Wildy disregards those nonconstructive approaches for this reason, pointing out that your + operation can't be effectively defined. You need to access the infinite to do anything but numbers defined via small complexity expression, say
[math] \pi = 2 \sum_{k=0}^\infty \frac{ 2^k (k!)^2 } { (2k+1)! } [/math]

>>7975744
Have you watched Wildburgers videos?

Anyway, what you say doesn't work: Take The sequence you defined and consider the New sequence
[math] V_n := U_n [/math] for n not 74
and
[math] V_{74} := -28 [/math].

This new seqeunce has the same limit but is different from the other "real number". You get to many terms in your theory.

People thus pull up an autistically large framework of set theory so they can define reals as equivalence classes of such sequences.
okay, then take this equivalence class definition of the reals.
Consider a sequence [math]W_n[/math] which for the first d=10^10^10^10^10^10^10^10 numbers are some random natural numbers and after [math]W_d[/math] you have [math]W_d:=U_d[/math]. Hence [math]W_n[/math] converges to your root two and thus is a representative of that equivalence class. However, if you had someone the sequence [math]W_n[/math] and ask him what number it represents, he can't tell you, because all that's accessible to him is random gibberisch. Wildy disregards those nonconstructive approaches for this reason, pointing out that your + operation can't be effectively defined. You need to access the infinite to do anything but numbers defined via small complexity expression, say
[math] \pi = 2 \sum_{k=0}^\infty \frac{ 2^k (k!)^2 } { (2k+1)! } [/math]