True by definition? "If 3 is an integer, and three is greater than zero, then 3 is a positive integer."

[PseuTonym]

Is the following statement true by definition?

“If 3 is an integer, and three is greater than zero, then 3 is a positive integer.”

 

[STT]

Is the following statement true by definition?

“If 3 is an integer, and three is greater than zero, then 3 is a positive integer.”

This is true intrinsically considering the fact that you need to add another integer to get from 0 to 3, this is very definition of greater.

 

[PseuTonym]

This is true intrinsically considering the fact that you need to add another integer to get from 0 to 3, this is very definition of greater.

Why can’t you subtract the integer known as “negative three” from zero to get from zero to three?

When you write “another integer”, do you simply mean an integer that isn’t equal to zero? Perhaps you can get from 0 to the integer known as “negative three” by starting with zero and adding the integer known as “negative three.”

What is the connection between the concept of “true intrinsically” and the concept of a “definition”?

If you start with zero and add integer multiples of the positive square root of two, then you will never get to an integer other than zero itself.

 

[STT]

Why can’t you subtract the integer known as “negative three” from zero to get from zero to three?

I believe that negative numbers are not real. We can always get ride of them with a change in reference point, zero.

When you write “another integer”, do you simply mean an integer that isn’t equal to zero?

Doesn’t that apply to all integer?

Perhaps you can get from 0 to the integer known as “negative three” by starting with zero and adding the integer known as “negative three.”

Negative three does not exist.

What is the connection between the concept of “true intrinsically” and the concept of a “definition”?

Because the concept of greater or smaller are real while we deal with positive integers.

If you start with zero and add integer multiples of the positive square root of two, then you will never get to an integer other than zero itself.

I don’t understand what you are trying to say here.

 

[Convert_in_99]

You’ve had some very interesting threads lately.

 

[Angela77]

I would say that it is true as long as we are defining “positive” as “greater than 0.”

 

[Beryllos]

I believe that negative numbers are not real. We can always get ride of them with a change in reference point, zero.

I would like to see you solve some simple physics problems with that approach. Consider, for example, an object traveling upward against the force of gravity, eventually stopping and then traveling downward. It would be tricky, to say the least, to switch your frame of reference when the motion reverses but the force does not reverse.

 

[STT]

I would like to see you solve some simple physics problems with that approach. Consider, for example, an object traveling upward against the force of gravity, eventually stopping and then traveling downward. It would be tricky, to say the least, to switch your frame of reference when the motion reverses but the force does not reverse.

Just think that the maximum velocity is V at starting and end points. Now add V to all velocity at any given time. This means that the velocity at the beginning and end points are 2V and zero respectively.

 

[Beryllos]

Just think that the maximum velocity is V at starting and end points. Now add V to all velocity at any given time. This means that the velocity at the beginning and end points are 2V and zero respectively.

Okay, you do it your way, and I’ll do it mine.

 

[PseuTonym]

I believe that negative numbers are not real. We can always get rid of them with a change in reference point, zero.

What if you are dealing with linear algebra, specifically the determinant of a so-called “square” matrix?

That a determinant is non-zero has special significance: it implies that the corresponding matrix is invertible. So in what sense can you simply “change the reference point”?

Link:
math.stackexchange.com/questions/355644/what-does-it-mean-to-have-a-determinant-equal-to-zero

There are so-called “definitions” of a determinant that are complicated computational methods that were invented after a more reasonable, conceptual definition was invented. Unfortunately, with the emphasis on computation in schools, there are people who know only about the complicated computational methods, and know nothing about any simple, conceptual definition. It would have been impossible to know that the computational methods always work, unless the conceptual definition had been invented.

The following book might be worth looking at:
linear.axler.net/

 

[STT]

What if you are dealing with linear algebra, specifically the determinant of a so-called “square” matrix?

That a determinant is non-zero has special significance: it implies that the corresponding matrix is invertible. So in what sense can you simply “change the reference point”?

Link:
math.stackexchange.com/questions/355644/what-does-it-mean-to-have-a-determinant-equal-to-zero

There are so-called “definitions” of a determinant that are complicated computational methods that were invented after a more reasonable, conceptual definition was invented. Unfortunately, with the emphasis on computation in schools, there are people who know only about the complicated computational methods, and know nothing about any simple, conceptual definition. It would have been impossible to know that the computational methods always work, unless the conceptual definition had been invented.

The following book might be worth looking at:
linear.axler.net/

Unfortunately I forgot all my knowledge about linear algebra. All I remember is that we can add a matrix lets say “a”.“1” where a is “a” positive constant and “1” is the unitary matrix to the original matrix such that the eigenvalues are shifted by “a” and the determinant of the matrix is shifted accordingly, (l1+a)(l2+a)…

 

[PseuTonym]

I believe that negative numbers are not real.

Michael Spivak gives the example of the following equation:

(x cubed) - 15x - 4 = 0

You can check for yourself that x = 4 is one of the solutions.

To discover what the solutions are, other than by trial and error, requires a method. You will never understand the method if you reject negative numbers.

Spivak shows a general method involving not merely negative numbers, but so-called “complex numbers.” To apply the method, there is an intermediate step involving observing that one of the cube roots of 2 + 11i is 2+i. The imaginary unit “i” cancels out of an expression that gives the particular solution x = 4.

The method is general in the sense that it doesn’t depend on the particular coefficients that the polynomial has: 1 for the 3rd power of x, 0 for the 2nd power of x, negative 15 for the 1st power of x, and negative four for the constant.

 

[Tomdstone]

Just think that the maximum velocity is V at starting and end points. Now add V to all velocity at any given time. This means that the velocity at the beginning and end points are 2V and zero respectively.

Not true if V = c, the speed of light.

 

[PseuTonym]

I believe that negative numbers are not real.

Consider the following formula:

pi/4 = 1 - (1/3) + (1/5) - (1/7) + (1/9) - (1/11) + (1/13) …

It is obtained from an infinite sum. In other words, only the operation of addition is involved. However, the numbers generated alternate between positive and negative, starting with the positive number one as the first term.

Is it possible to develop a theory of expressions involving an infinite sequence of addition and subtraction operations? You could try to invent such a theory. Otherwise, there is no way to explain the above formula within your system of thinking.

 

[Qoeleth]

It seems to be a ill-constructed poll- as it is not possible to give a simple affirmative, to the effect the “Yes, if 3 is an integer, etc.”

This leads me to suspect it is actually a kind of psychological experiment. Would this be correct?

 

[fisherman_carl]

Three is only greater than zero when you are in the mood to increase. But not when you are in the mood to decrease like in a game of golf.

 

[Bradski]

You’re on the wrong forum.

 

[inocente]

I believe that negative numbers are not real. We can always get ride of them with a change in reference point, zero.

Zero and i, the square root of minus one, are the only necessary numbers. For 1 = 0 - i[sup]2[/sup] and so on.

 

[PseuTonym]

I believe that negative numbers are not real.

Do you believe that zero is a real number?

In ordinary mathematical language, zero is said to be a “non-negative integer”, but zero isn’t a positive integer.

 

[STT]

Do you believe that zero is a real number?

In ordinary mathematical language, zero is said to be a “non-negative integer”, but zero isn’t a positive integer.

I think that zero is not a real number. It only indicates absence of anything.