There is an infinite number of numbers between 0 and 1. What does this mean for science?

There is an infinite number of numbers between 0 and 1. What does this mean for science?

Countable & Uncountable Infinities

Previous questionCan a melancholic man be made sanguine or choleric through testosterone therapy and gaining self-confidence?
Next questionWhat diet should you follow and what exercises should you do in order for the abs to become prominent at home?

answers (2)

Answer 1
January, 2021

We can say that it matters in the sense that it allows you to compare the segment from 0 to 1 with the set of all real numbers and conclude that they are of equal power. Indeed, it is quite easy to establish a one-to-one correspondence between them, for example, like this: y = log ((1 - x) / x), where x is a number from the interval (0, 1), and y is any real number. If you want to include the boundaries of the interval, you can expand the corresponding set of real numbers with infinities.

Here's a fun fact - one set is a subset of another, and they have the same cardinality. The same trick can be performed with a set of natural numbers, removing from there, for example, all even ones.

Answer 2
January, 2021

This is another achievement of science. It can be the pride of the scientific world, proving the limitless possibilities of scientific thought. This is a fundamental knowledge that every person who respects science should know.

And so nothing.

Related question

If the universe is infinite, does this mean that there is any object that can appear in our imagination?

Read more

What does the diagnosis of Hypertension grade 1, risk 4 mean for a person? What limits to set for yourself and what is the optimal lifestyle?

Read more

Passed an analysis for COVID-19 IgG antibodies. The result is positive 3.07 and negative 1.40, what does this mean?

Read more

Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

Is it scientific to believe that there are an infinite number of gender categories in the world (eg biggender, agender, etc.)?

Read more

What will happen if an infinitely strong fist is hitting an infinitely strong e% against an infinitely strong e% alnik?

Read more

Why is there still no cure for herpes and what does the almost widespread infection of mankind with this virus mean? How dire are the consequences?

Read more

Scientists have removed HIV from the DNA of mice for the first time. Does this mean that soon science will defeat this disease?

Read more

What factors reduce the number of abortions? Is there an effective government program that has reduced the number of abortions?

Read more

One Solution, No Solution, or Infinitely Many Solutions - Consistent & Inconsistent Systems

How does science explain the placebo effect? Does this mean that a person's faith is as important as the material views of scientists?

Read more

If an expensive butter has a shelf life of 1 year, does that mean it contains palm oil?

Read more

Everything is infinitely increasing and decreasing, everything is motionless and at the same time dynamic, there is no limit. What to do with this information?

Read more

An adult has increased lymphocytes in the blood, what does this mean?

Read more

If Coca-Cola Zero has no sugar and only 1 calorie, does this mean that it will not deteriorate teeth and increase weight?

Read more

How To Count Past Infinity

Why, despite the low infection rate of HIV (0.1% / 1%), the number of cases is growing, acquiring the character of an epidemic?

Read more

What is the evolutionary meaning of the large number of pain receptors in the gums?

Read more

What is an electronic cigarette? What types are there and what does it consist of?

Read more

Why is there an odd number of lenses in the gift lens pack?

Read more

What does this gesture mean?

Read more

Bijection between (0,1) and (-inf, inf)

Now there are a large number of cigarettes with a button, does this make cigarettes even more harmful?

Read more

What does trainspotting mean? How does this relate to the film of the same name and English culture?

Read more