____ played a significant role in the construction of the Central Pacific (West to East) track of the Transcontinental Railroad, while ____ played a significant role in the construction of the Union Pacific (East to West) track.

Question

Word bank: Chinese immigrants, Native Americans, Irish immigrants, Japanese immigrants

Answer 1

Chinese immigrants played a significant role in the construction of the Central Pacific (West to East) track of the Transcontinental Railroad, while Irish immigrants played a significant role in the construction of the Union Pacific (East to West) track.

Answer 2

Whats 2+2

Answer 3

2 + 2 equals 4.

Answer 4

No I think your wrong

Answer 5

In standard arithmetic, 2 + 2 equals 4. If you have a different context or perspective in mind, please share it!

Answer 6

This can be possible only if we suppose that both the 2s are rounded nos. If you do 2.4 rounded (2) + 2.2 rounded (2), you get 4.6 which rounds to 5

Answer 7

You're correct that rounding can lead to different interpretations. If you're considering 2.4 rounded to 2 and 2.2 rounded to 2, the rounding process can affect the result of addition, which could lead to a summed total that, when rounded, may arrive at a different integer.

So, while in straightforward arithmetic, 2 + 2 equals 4, incorporating rounding and approximations can lead to different conclusions. Thank you for pointing that out!

Answer 8

Theorem: Let 2 be a Cauchy real number, and 4 a rational number. The Cauchy real number represented by 2+2 is not equal to the rational number 4. Of course, the real number 2+2 is equal to the real number 4, this is in some sense a definition.Apr 2, 2022

Answer 9

The theorem you've mentioned touches on the distinction between how numbers can be defined and represented in different mathematical systems. Let's clarify a few points:

1. Cauchy Real Numbers: In the context of real analysis, Cauchy sequences provide a way to define real numbers formally. A Cauchy real number is defined via sequences of rational numbers that converge. The number 2, represented as a Cauchy sequence, remains the same regardless of how it's defined.

2. Rational Numbers: Rational numbers are simply ratios of integers. The number 4 is a rational number and is represented in the set of rational numbers as the fraction \( \frac{4}{1} \).

3. Addition and Equivalence: In standard arithmetic, adding 2 (a real number, potentially represented as a Cauchy sequence) and 2 yields 4 (a rational number), and in typical mathematical contexts, these are equivalent. The operations of addition and equality between the two number types are consistent.

4. Different Representations: While you may refer to the Cauchy real number defined as "2 + 2" and claim it does not equal the rational number "4," such a conclusion would typically arise from specific definitions or interpretations in a particular mathematical framework. However, generally speaking, within conventional mathematics, the two results are understood to be equivalent.

If you have a specific theoretical framework or a more nuanced argument in play, I would be interested to hear more about it. These kinds of explorations can be quite fascinating in advanced mathematical discussions!