Certain Quote by Georg Cantor
“I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.”
About This Quote
Source Lecture: Foundations of Set Theory, 1883
He acknowledges opposing mainstream views on infinity and the nature of numbers, defending his own perspective.
In simple terms: Challenging common beliefs about infinity
Key Takeaway
Question established ideas on mathematical concepts
Themes
philosophy
mathematics
infinity
Mood
analytical
reflective
Type
academic
philosophical
When to use this quote
- academic research
- philosophical discourse
- teaching
- public lectures
Key Concepts
set theory
ontological debate
Questions to Reflect On
- What assumptions about numbers do we take for granted?
- How can we reconcile intuition with formal theory?
A Different Perspective
Infinite concepts can be abstract and hard to grasp for many
![“...There is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being…” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/bc5/james-joseph-sylvester-23602_action_there-is-no-study-in-the-world-which-bri_23809.jpg)
![“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately…” quote by Georg Cantor](https://sms4smile.com/quotes/img-quotes/1c9/georg-cantor-20252_axioms_the-old-and-oft-repeated-proposition-tot_1288544.jpg)
