Negation of a mathematical statement containing the word: but finitely many

Asked Nov 25 '19 at 16:27

Active Nov 25 '19 at 16:33

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I have a mathematical statement of the form:

Case: Fix $ε>0$ and three distinct elements $b₁,b₂,b₃$ in a set $A$. Then all but finitely many $q∈A$ satisfy: $$(1-ε)a_{q}<c_{q}$$

where $a_{q}$ and $c_{q}$ are real sequences.

Then my question is to find the negation of this case.

edited Nov 25 '19 at 16:33

asked Nov 25 '19 at 16:27

Safwane

2

Begin by stating precisely what "all but finitely many" means. – Andrés E. Caicedo Nov 25 '19 at 16:30
1

"all but finitely many" – Mauro ALLEGRANZA Nov 25 '19 at 16:31
If you copy and paste here, please at least check the text that you pasted. You're missing a "fi" ligature in the title. – joriki Nov 25 '19 at 16:32
@MauroALLEGRANZA: Yes, I understood that it means that the statement is true in all cases, except that there might be some finite number of exceptions. – Safwane Nov 25 '19 at 16:43
The negation of "all but finitely many" will be "finitely many". – Mauro ALLEGRANZA Nov 25 '19 at 21:16

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