I came across an estimation of the relative error between two representations of the same number, one implemented in C++ and another one via a computer algebra program, that was in units of machine epsilon. My question is trivial, though I wasn’t able to find an answer:

If I say that the number has 3 machine epsilons relative error, how many digits does it mean that the approximated number looses compared to the true number?

# Tag: epsilon

## floating point – What is the machine epsilon and number of mantissa bits for TI-83?

I am trying to determine how many bits the TI-83 Plus uses to store floating point numbers. I am using the algorithm for approximating the machine epsilon given in “Numerical Mathematics and Computing” by Cheney and Kincaid. In TI-BASIC, it looks like this:

```
: 1 -> E
: While (1+E) > 1
: E/2 -> E
: End
: Disp 2*E
```

The program returns 9.31322575E-10, which is equal to $2^{-30}$. This is an approximation within a factor of 2.

Here’s where I get confused. In the textbook I mentioned above, they say that the number of binary digits used in the mantissa, $k$, is given by $u=2^{-k}$, where $u$ is the number we just found. This is easy to verify for things like IEEE-754 format, because the mantissa is stored as its base 2 representation, so k is the number of bits allocated to the mantissa. However, as far as I can tell from sources like this, the TI-83 does not use IEEE-754 floating point, but different floating point encoding scheme with 7 bytes of binary-coded decimal for the mantissa (that’s 14 decimal digits). If that is true, then it seems to me like the machine epsilon should be $10^{-14}$. Furthermore, this means the number of mantissa bits is 56, rather than 30.

How can I rectify these two things?

## PDA for $ S to S0S1S0S mid S0S0S1S mid S1S0S0S mid epsilon $

How do I design a pushdown automaton for the language described by the following grammar?

$$ S to S0S1S0S mid S0S0S1S mid S1S0S0S mid epsilon $$

I tried converting the grammar to CNF, but didn’t get the correct answer.

## limits – Why can Epsilon equal the absolute value of the function divided by 2? ($epsilon = frac{|f(point of interest)|}{2} > 0$)

I am trying to solve a tricky textbook problem that requires the use of the epsilon-delta definition of a limit. However, with my elementary understanding of how to answer these kinds of problems, the solution on the back of the book begins its solution by stating something along these lines:

*Since f(point of interest) can’t be 0 (in this question’s scenario), and the function is continuous on the point of interest, then you can say:*

**$epsilon = frac{|f(point of interest)|}{2} > 0$**

How is this possible? Correct me if I’m wrong, but I thought epsilon was only calculable through direct manipulation of delta. How can you make this deduction without delta, just from knowing that the function at a point of interest can’t be 0?

Any help please? Thank you.

## Looking for a grammar to ${w, epsilon left { a, b, c right }^{*} /w= a^ {n} b^ {2n+1} c^ {n} a^ {n-1} ,|,,n $ > $ 1}$

I’ve tried so many times to look for a grammar for this language ${w, epsilon left { a, b, c right }^{*} /w= a^ {n} b^ {2n+1} c^ {n} a^ {n-1} ,|,,n $ > $ 1}$ but I couldn’t find it. Anyone have an idea on how to solve it?

## grammar for the language ${w, epsilon left { a,b,c right }^{*} /w= a^{n} b^{2n-1} c^{n} a^{n+1} ,|,,n ,$>$, 1}$

i’ve been trying to find a grammar for this language ${w, epsilon left { a,b,c right }^{*} /w= a^{n} b^{2n-1} c^{n} a^{n+1} ,|,,n ,$>$, 1}$

can anyone have a solution ?

## Epsilon – Epsilon.icu

**I am not the admin or the owner of the project, I don’t know the admin!**

**Started:** Friday, 18 December 2020**Payouts:** Manual (up to 24 hours, min withdrawal amounts are: 1 USD, 0.0001 BTC, 0.002 ETH, 0.01 LTC, 0.008 DASH, 0.003 BCH, 1.5 XRP, 0.0075 XMR)**Ref-offer** 5% – 2% – 1%

**Technical details** (information from ISP and HyipLogs resources):

**Domain**: Namecheap, 2020-12-09 – 2021-12-09 (registered for 1 year)**SSL**: Sectigo RSA Domain Validation Secure Server CA valid from 09 Dec, 2020 to 07 Feb, 2021 – Sectigo Limited**Hosting**: Namecheap, Inc**IP-address**: 199.192.18.36 (United States / Newark) IP not used in other projects**Script**: not defined**Simillar text HYIPs**: 0**Simillar design HYIPs**: 0

**Description:**

QUOTE

Epsilon is an innovative and practical “digital funds” platform online, which welcomes all members worldwide. We act solely as a facilitator between you (our members) and the Enterprise (our investment). Our key objective is to constantly increase the mutual return on investment through Epsilon Platform. To achieve that goal, we’re prepared to deliver you an extremely high returns of 22% daily and 154% after 5 days for buying digital funds in our platform via the eWallets we accept, and per the terms presented in our Investment Plans.Opening Account with us is completely free and fully confidential, with our strict security protocols to validate transactions authenticity & safeguard sensitive info.

**Accepts:**

Bitcoin, Ethereum, Litecoin, Perfect Money, Bitcoin Cash, Dash, Ripple (XRP), Monero (XMR)

**Perfect Money:**

- U25782699 (Epsilon) – Russian Federation –
**Verified**– 08.11.2017 – 7 point(s)

**Investment plans:**

- $10 – $200000: 22% daily for 7 days (deposit included)
- $10 – $200000: 154% after 5 days

**Registered company profile:** https://find-and-update.company-information…ompany/12445548**Company Address:** https://goo.gl/maps/yWvMrgwQzpziR6Vg8**Telegram:** https://t.me/epsilon_icu**Telegram:** https://t.me/epsilon_admin**Twitter:** https://twitter.com/Epsilon_icu**Youtube:** https://www.youtube.com/channel/UCbfjwtoixKV17UA5Wik38Zw**Presentation:** https://www.youtube.com/watch?v=8Rh3tGPbcPs

QUOTE

150.00 USD: The amount of 150.00 USD has been withdrawn from your account. Accounts: U19811025->U25782699. Memo: Shopping Cart Payment. https//epsilon.icu/.. Date: 18:18 18.12.20. Batch: 355924659.

*This topic was created for the purpose of information. I am not responsible for your decisions!*

This post has been edited by **Instant-Monitor.com**: Yesterday, 07:25 PM

## compiladores – Como se simula a transição épsilon na codificação C?

Obrigado por contribuir com o Stack Overflow em Português!

- Certifique-se de
*responder à pergunta*. Entre em detalhes sobre a sua solução e compartilhe o que você descobriu.

Mas *evite* …

- Pedir esclarecimentos ou detalhes sobre outras respostas.
- Fazer afirmações baseadas apenas na sua opinião; aponte referências ou experiências anteriores.

Para aprender mais, veja nossas dicas sobre como escrever boas respostas.

## inequality – If $|a-b| leq frac{epsilon}{2}$ and $|a| gt epsilon$, constructively prove that $|b|geq frac{epsilon}{2}$.

You have to use the inverse triangle inequality, that is for any real numbers $a$ and $b$ we have

$$|a|-|b| leq |a-b|.$$

On the one hand,

$$|a|-|b| leq |a-b|leq frac{varepsilon}{2}.$$

Hence,

$$|a|leq |b|+frac{varepsilon}{2}.$$

Also $|a|>varepsilon$, so

$$varepsilon<|a|leq |b|+frac{varepsilon}{2}.$$

In particular,

$$varepsilon<|b|+frac{varepsilon}{2},$$

where the inequality is strict because of the fact that $varepsilon<|a|$, and the result is proven:

$$|b|>frac{varepsilon}{2}.$$

## calculus of variations – epsilon delta proof of limit

I am trying to learn the epsilon delta proof of limit. I am a little confused why we always consider that epsilon>0, like if the discontinuity point of the graph is below the x axis, then nearest value or range to limit will also be in the negative part, in that case value of epsilon will be smaller than zero.