Are all irrational numbers rational?

AI Thread Summary
Irrational numbers, such as pi, cannot be expressed as fractions of integers, which defines rational numbers. The discussion highlights a misunderstanding regarding the nature of pi as a ratio of circumference to diameter, emphasizing that this ratio does not yield a fraction of integers. It is clarified that the existence of a rational circle with both rational circumference and diameter is not possible. The conversation also touches on the broader implications of definitions in mathematics. Ultimately, all irrational numbers remain non-rational by their very nature.
Skhandelwal
Messages
400
Reaction score
3
Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
 
Mathematics news on Phys.org
Skhandelwal said:
Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?

Short answer: No.

Tongue-in-cheek answer: Yes, but the fraction would have at least one noninteger.

Longer answer: You're wrongly assuming that a circle with rational circumference and diameter exists.
 
? are all humans non human? are all m ortals immortal? are al...
 
mathwonk said:
? are all humans non human? are all m ortals immortal? are al...

lol :smile:
 
Skhandelwal said:
Since pie is the ratio of the circumference of the circle to its diameter, isn't it possible that there exist a fraction for all nonrepeating going on forever decimal values?
The definition of "rational number" is that it can be written as a fraction with numerator and denominator integers. The "ratio of the circumference of the circle to its diameter" is not a ratio of integers.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

I Is the Ratio of Circumference to Radius of a Circle Always Irrational?
Replies
19
Views
3K
B Is PI (##\pi##) really a number?
Replies
28
Views
2K
I Generating Irrational Ratios in Wave Simulations
Replies
6
Views
2K
B Proving the area formula for a rectangle for all positive real numbers
Replies
10
Views
2K
I Rational powers of irrational numbers
Replies
27
Views
3K
I Proof of a fact about real numbers - transcendental and algebraic
Replies
7
Views
1K
MHB How Can Rational and Irrational Numbers Combine in Arithmetic Operations?
Replies
16
Views
3K
I Rational sequence converging to irrational
Replies
13
Views
8K
MHB Is 7 an irrational number in the set of integers?
Replies
5
Views
3K
MHB Is (27/4)/(6.75) a Whole, Natural, Integer, Rational, or Irrational Number?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top