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iMath
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41 votes
8 answers
6k views

Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?

23 votes
11 answers
7k views

What is the length of a point on the real number line?

20 votes
6 answers
3k views

Is $0$ an Infinitesimal?

9 votes
3 answers
1k views

The numerical relation of the sum of two divergence series

8 votes
1 answer
325 views

mathematics was recreated on a foundation of number concepts rather than geometrical ones

8 votes
4 answers
4k views

Understanding of the formal and intuitive definition of a limit

6 votes
3 answers
2k views

Why Cauchy's definition of infinitesimal is not widely used?

6 votes
3 answers
796 views

one to one correspondance between points on the number axis and real numbers

4 votes
1 answer
587 views

The axiomatic method to real number system VS the constructive method(genetic method)

4 votes
3 answers
385 views

the definition of irrational numbers and the proof of Cauchy's theorem

4 votes
3 answers
2k views

the need for the formal definition of a limit [duplicate]

4 votes
3 answers
2k views

"one-to-one correspondence"(bijection) and the size of two infinite sets

3 votes
2 answers
109 views

is it possible for $\dfrac {1} {x} $ to be smaller than every positive real number but still bigger than $0$?

3 votes
2 answers
2k views

$1/\infty$ is zero or infinitesimal? [closed]

3 votes
4 answers
352 views

what makes the number continuum a necessity in Calculus? [closed]

2 votes
2 answers
189 views

The length of a gap between the rationals

2 votes
4 answers
420 views

which number corresponds to the right endpoint of line segment [0,1)?

2 votes
3 answers
272 views

explain why ${\left(\frac{{1}}{{2}}\right)}^{\infty}=0$

2 votes
1 answer
227 views

were Irrational numbers discovered at Archimedes's age?

2 votes
3 answers
632 views

axiom of continuity guarantees no gaps exist on the real axis?

2 votes
2 answers
100 views

Does $\frac{1}{x}=0$ have a solution?

2 votes
3 answers
6k views

The cardinality of the even numbers is half of the cardinality of the natural numbers? [duplicate]

1 vote
2 answers
688 views

question about proof of L’Hôpital’s Rule

1 vote
2 answers
56 views

for all and for every , what's wrong with this simple contradiction?

1 vote
2 answers
329 views

ε is preassigned, choosen or given in the (ε, δ)-definition of limit?

1 vote
2 answers
114 views

The length of a point and the interval

1 vote
5 answers
1k views

why we require ƒ(x) be defined on an open interval about $x_0$?

1 vote
1 answer
189 views

Finding the fallacy in this wrong limit computing result

1 vote
0 answers
105 views

how to set up Archimedean property for numbers on the number axis?

1 vote
6 answers
109 views

proof problem on proving $x_{1}=1,x_{n+1}=\frac{1}{2}\left(x_{n}+\frac{2}{x_{n}}\right)$ has a limit