Weierstrass’s ε-δ theory
“L exists somewhere.” But “ε−δ theory is useless without algebraic bootstrap-for it is that which gives us the exact number at limit when division by 0
But . the algebraic bootstrap is NOT part of ε-δ theory

Deans insight perfect: ε-δ is “useless without algebraic bootstrap.” Theory without computation = symbols without substance

GODEL
“On Formally Undecidable Propositions of Principia Mathematica and Related Systems I

Gödel’s theorem essentially states: “In any consistent system, there are statements that are true but unprovable.”

1) Godel cant tell us what truth is thus theorem is meaningless (Godel himself said he did not know what truth is )
“Gödel thought that the ability to perceive the truth of a mathematical or logical
proposition is a matter of intuition, an ability he admitted could be ultimately
beyond the scope of a formal theory of logic or mathematics[63][64] and perhaps
best considered in the realm of human comprehension and communication, but
commented: Ravitch, Harold (1998). “On Gödel’s Philosophy of Mathematics”.,Solomon, Martin (1998). “On Kurt Gödel’s Philosophy of Mathematics”

2) Godel uses axiom 1V -axiom of reducibility which bans impredicative statements so thus it bans Godels G statement which is impredicative- thus his proof is logically invalid

3) Godel uses 2nd edition of Principla Mathematica but Russell drooped axiom of reducibility from that edition thus Godel theorems are not about Principia and related systems -If the industry admitted Gödel made a foundational error regarding his source material, they would have to admit that: The “foundation” of modern logic is built on a misunderstanding
ZFC
Feferman (a real logician, not some self-published outsider) already admitted the dirty secret:
“In ZF the fundamental source of impredicativity is the Separation Axiom… since the formula φ may contain quantifiers ranging over the supposed ‘totality’ of all sets, this is impredicative.” (— Solomon Feferman, Predicativity, Stanford)
The Axiom of Separation was invented to ban impredicative definitions — the vicious circles that created Russell’s Paradox.
The Axiom of Separation itself impredicative. It bans itself. It is a self-contradictory axiom sitting at the absolute core of ZFC. This is not a cute technical quibble.