Abstract Algebra

Yes 93.4 is greater than 93.0

Some sequences are defined by rules and algebra is a mathematical way of describing rules.

Yes, you could let H be a separable Hilbert space. Then what?

45x20y5 / 5x4y = 45/5*x20-4*y5-1 = 9x16y4

The order of a cyclic group is the number of distinct elements in the group. It is also the smallest power, k, such that xk = i for all elements x in the group (i is the identity).

With an A mint mark, about $12 in worn condition, up to $35 with only moderate wear.

Other mint marks are in the $15-$40 range.

It is a system of logical calculus on which logic axioms are based on.

4

Parity refers to whether an integer is odd or even.

i have always questioned this myself but it is necessary to solve everyday problems. for example: you need to split 24 apples evenly among 8 people. so you use the equation

8x = 24 to find an answer of 3 apples per person.

The answer depends on

1. how good you are,

2. where in the world you work,

3. how many lucky breaks you get.

No one can, for three reasons.

Reason 1: There are several long-standing unsolved problems in mathematics. Since they are unsolved, nobody knows how hard they are.

Reason 2: What one person may find hard can seem trivially easy to another. But that other person may find something hard that the first would find simple.

Reason 3: There may be new problems waiting to be discovered.

99x99x99

Yes, it should be non-zero; if you multiply both sides by zero you wipe out the equation.

It is approximately 5.66

The decimal notation for 418/580 is 0.7206896552

1.6 repeating

In classical studies, it is also called a postulate.

Depends on condition, box, papers, etc. Range from 100-700 USD.

yes. to understand the higher maths you need pre algebra

The Seven Identity Theorem has a long history. It was created in 237 BC by Greek scientist, Archimedes.

On July 7th of 237, Archimedes reportedly woke from a dream. As his close friend, Conon of Samos, reports, the dream consisted of an army of Alexandrians who repeatedly mocked him. One Alexandrian stepped forward and declared, "What does he know? Naught! Dost he understand the true natures of this world? I trow not!" Afterwords, the Alexandrians began whispering the number, "7", over and over again.

In the dream, Archimedes was thoroughly confused about the number 7, wondering if it possibly had an unique identity. He began extensive research on this number.

He made seven immediate connections, some of which are listed: there are 7 days in the week, 7 notes on the musical scale, 7 directions (left, right, up, down, forward, back, center), and so forth.

Interested in geometry, Archimedes made another connection: imagine a cube, which has six sides. Imagine the largest sphere possible fully enclosed within the cube. This is one of the many examples demonstrating that such a figure with six sides will always fit around a seventh figure. Similarly, if a circle of any particular size is drawn, you can draw exactly six circles of the same size around that central circle. You can draw no more and no less if you want each circle to be externally tangent to at least three neighboring circles.

Archimedes proceeded to discovering that if a projectile is launched upwards with a minimum velocity of 49 meters per seconds, the vertex of the trajectory always exceeds 7 meters. This is due to the nature of gravity on Earth. Interestingly, if a projectile is launched upwards with a minimum velocity of 343 meters per seconds, the vertex of the trajectory always exceeds 77 meters.

Around this time, he began experimenting with water displacement and buoyancy. He found that if an object with a mass of 7 grams is released into a container holding precisely 2401 liters of water, the water displaced will be equal to (7*10^-4) liters. If an object with a mass of 7497 grams is released into the same container, the water displaced will be equal to 727 liters.

There are countless applications of the number, "7", in our modern world. The majority of them were discovered by Archimedes. Before he died, he compiled a book plainly titled, "Seven". Inside the book, he compiled his most important discoveries into a list and named the endless ability to generate such useful applications "the Seven Identity Theorem".

When Archimedes died in 212 B.C., the book was found and published. However, people were appalled at the fact that this seemingly normal number, 7, would have so many useful applications. They felt degraded, knowing that they had used the number so many times in their lifetimes without knowing its deeper meaning. To this day, many refuse to speak of it, as doing so would bring back such memories of humiliation.

Nevertheless, nearly all professional mathematicians use the Seven Identity Theorem daily to solve complex problems. To mathematicians, Archimedes is considered the most prominent figure in history for discovering such a valuable theorem and unearthing the mystery of the number, 7.

100-340 or so

154a - 5 is not an equation, as there is no relation between two unknowns, or an unknown or a known.

But to answer your question, 5 is always equal to 5, except when 5 is a constant function, in which case it is a function which is always equal to 5, but is not 5 itself - because 5 itself is a scalar while the function 5 is a function.